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The Railroad Lubricant-testing Machine. 

[As built by the Pratt & Whitney Co.] 



A TREATISE 



ON 



FRICTION AND LOST WORK 



IN 



Machinery and Millwork. 



BY 

ROBERT H. THURSTON, A.M., C.E., 

Professor of Engineering at the Stevens Institute of Technology ; Past President 

of the American Society of Mechanical Engineers, etc., etc.; Author 

of Materials of Engineering, History of the Steam 

Engine, etc., etc. 



1 






r 




/ 



NEW YORK : 
JOHN WILEY & SONS 

1885. 



s 



Copyright, 1885, by ROBERT H. THURSTON. 



All rights reserved. 




M. H. GREEN, 

Printer, Electrotyper and Binder, 
74 and 76 Beekman Street, 

NEW YORK. 



TO 

THE ENGINEER, PHYSICIST AND MATHEMATICIAN 

G. A. HIRN, 

ONE OF THE EARLIEST WORKERS IN THIS FIELD, 

JFiHS Little Worft 

IS INSCRIBED, IN GRATEFUL APPRECIATION OF PERSONAL, AS WELL 

AS OF PROFESSIONAL, AID AND ENCOURAGEMENT, AND IN 

RECOGNITION OF A MOST STIMULATING EXAMPLE 

OF NOBLE WORK, INSPIRED BY NOBLER 

THOUGHTS AND NOBLEST AIMS. 



PREFACE 



The following pages contain the results of an attempt to 
exhibit the facts and laws involved in the waste of energy by 
friction in machinery and mill-work. It is readily seen that in 
all well-designed machinery friction is the sole cause of lost 
work. The other possible cause, the permanent deformation 
of parts, cannot in such cases exist : every piece which is 
altered in shape by the forces received and transmitted, since 
it is never sprung beyond the elastic limit, restores by its 
restoration of form all energy expended in its alteration. 
Hence, the study of the methods and magnitudes of friction- 
losses, and the laws governing their production, is, next to the 
theory of pure mechanism, the most important study in rela- 
tion to the transmission of energy by machinery. 

In the endeavor to reconcile the facts of common experience 
with the data supplied by the working library of the engineer, 
and in the attempt to secure additional essential experimental 
data relating to lubricated surfaces, the Author was led into a 
series of investigations which revealed new facts and estab- 
lished the inapplicability of the usually received values of the 
coefficients of friction to much of the most familiar work of 
the engineer. The enormous variations observed in their 
values, as produced by change of pressure, of speed, and of 
temperature, and revealed by such investigations, compelled 
the Author to devise new apparatus and new methods of ex- 
periment, and finally led to the accumulation of a large mass 
of new and practically applicable data, the most important of 
which may be found here published. 



IV PREFACE. 

To make the work complete, it has been attempted to ex- 
hibit, as concisely as possible, the principles involved in the 
transmission of power and the performance of work, and in 
the waste of power by friction. It has also been attempted 
to show what are the methods of reducing such wastes, how to 
determine the purity and the intrinsic values of the unguents, 
and finally to ascertain how and to what extent variations of 
the magnitudes of these wastes are produced by variations of 
the conditions affecting the machinery exhibiting them. 

A large proportion of the work consists of new matter 
containing new data obtained by new investigations, and ex- 
hibiting variations from the formerly accepted laws of friction 
by new methods. Of this new matter a part has been pub- 
lished in an earlier work,* which contains the substance of 
lectures given by the Author before the Master Car-builders' 
Association and elsewhere. The present work is much more 
extensive, and in it the endeavor has been made to bring the 
subject fully up to date. The last chapter, which treats of 
the real value of lubricants, contains a development of prin- 
ciples enunciated in the earlier work, but never before fully 
worked into a consistent algebraic theory, with illustrations 
of its practical application. 

The experience and observation of the Author during a 
quarter of a century of work in the mechanical branches of 
engineering, in the design and practical construction and in 
the management of steam and other machinery, have impressed 
upon him the necessity of the study by the engineer of the 
nature, causes, and remedies, of lost work in mechanism, so 
strongly, that his expression of such views as are here pre- 
sented may sometimes appear to give an exaggerated idea 
of the importance of this division of the subject ; but in his 
opinion it would be very difficult to impress this matter too 
strongly upon the mind of the student or of the young en- 
gineer. 

It is his hope that the following pages may prove valuable 



* Friction and Lubrication. Railroad Gazette Publication Co., New York, 
1879. i2mo, pp. 212. 



PREFACE. V 

to the student, to the practising engineer, and to the man of 
science. The book is planned with a view to its use both as a 
text-book and as an office hand-book. 

The Author is greatly indebted to his colleagues, Professors 
Albert R. Leeds and C. A. Carr, U.S.N., for their kindness in 
assisting him in reading proof-sheets. 

Stevens Institute of Technology, 
Hoboken, N. J., April, 1885. 



CONTENTS, 



CHAPTER I. 

THEORY OF MACHINERY — ITS ACTION AND ITS EFFICIENCY. 

ART. PAGE 

i. Uses of Mechanism i 

2. Work of Machines — Machinery Classified i 

3. Power Demanded in Operating Machinery 2 

4. Work Defined — Diagrams of Work 3 

5. Power Defined 5 

6. Driving and Resisting Forces — Effort — Resistance 6 

7. Energy Defined — Actual and Potential Energy 6 

8. Law of Persistence of Energy — Energy and Work 8 

9. Acceleration and Retardation 9 

10. Storage and Restoration of Energy — Uniform Speed 9 

11. Useful and Lost Work 10 

12. Efficiency of Mechanism — Friction the one cause of its Reduction 10 

13. Magnitude of the Lost Work of Friction in Machinery and Mill-work. . 12 



CHAPTER II. 

NATURE, LAWS, AND THEORY OF FRICTION. 

14. Friction and its Causes — Kinds of Friction 14 

15. Moving and Resisting Forces — Force of Friction 15 

16. Solid Friction — Sliding and Rolling Friction , 16 

17. Laws of Sliding Friction 16 

18. Coefficients of Friction 17 

19. Methods of determining Coefficients 18 

20. Angle of Friction — Cone of Resistance 20 

21. Static Friction, or Friction of Rest 21 

22. Kinetic Friction, or Friction of Motion 21 

23. Distinctive Differences 22 

24. Principles of Equilibrium 23 

25. Solids at Rest on Rough Surfaces 23 



Vlll CONTENTS. 

ART. PAGE 

26. Examples of Application 25 

27. Solids in Motion on Rough Surface — Work 31 

28. Distribution of Pressure— Method of Wear 37 

29. Friction of Journals — Length of Journal — Shafting 40 

30. Friction of Pivots and Collars 54 

31. Friction of Belts and Cords 64 

32. Friction of Wedges and Screws — Couplings 71 

33. Friction of Gearing — Screw-gearing 73 

34. Rigidity of Cordage ; its Character 75 

35. Rigidity of Cordage ; its Laws 76 

36. Friction of Pulleys 79 

37. Friction of Systems of Pulleys 79 

38. Rolling Friction ; its Nature — Friction-wheels 80 

39. Rolling Friction ; its Laws — Friction-gearing 82 

40. Draught of Vehicles 84 

41. Friction of Earth — Foundations 85 

42. Pressure on Retaining Walls 89 

43. Fluid Friction ; its Nature 96 

44. Fluid Friction ; its Laws 97 

45. Influence of Viscosity and Density . 98 

46. Molecular, or Internal Friction 99 

47. Complex Friction — Lubrication — Laws 99 

48. Lubricated Surfaces — Limits of Pressure 101 

49. Magnitudes and Methods of Reduction of Wastes of Energy 102 



CHAPTER III. 

LUBRICANTS. 

50. Lubricants ; their Characteristics and Uses 104 

51. Valuable Qualities of Lubricants 104 

52. Lubricants Classed — The Oils no 

53. The Semi-fluid Lubricants — Tallow 112 

54. The Semi-solid Lubricants — Hard Greases 113 

55. The Solid Lubricants — Graphite, Soapstone, etc . 115 

56. Animal Oils 117 

57. Sperm Oil— Whale Oil 117 

58. Lard Oil 118 

59. Neat's-foot Oil— Tallow Oil 119 

60. Fish Oils. 119 

61. Vegetable Oils 120 

62. Olive Oil 121 

63. Cotton-seed Oil 123 

64. Rape-seed Oil 123 

65. Colza Oil 124 

66. Palm Oil 124 



CONTENTS. IX 

ART. PAGE 

67. Cocoa-nut Oil 125 

68. Elaine Oil 125 

69. Pea-nut Oil, or Ground-nut Oil 126 

70. Castor Oil 126 

71. Linseed Oil 127 

72. Mineral Oils, or Petroleums 127 

73. Well Oils 129 

74. Shale Oils 129 

75. Refined Petroleums — Mixing Lubricants „ 130 

76. Purification — Cleansing Oils 133 



CHAPTER IV. 

LUBRICATION — APPARATUS. 

77. Methods of applying Lubricants , 137 

78. Use of Solid Lubricants 138 

79. Applying Semi-solid Lubricants 138 

80. Methods of Oiling 139 

81. Forms of Grease Cup 141 

82. Styles of Oil Cup 143 

83. Lubricating Moving Parts 146 

84. Hand Apparatus 148 

85. Oil Pumps 149 

86. "Water Bearings" , 150 

87. Cooled Bearings, unlubricated 150 

88. Bearing Surfaces and Materials , 150 

CHAPTER V. 

CHEMICAL AND PHYSICAL TESTS OF OILS. 

89. Methods of Examination of Oils 153 

90. Detection of Adulteration 154 

91. Chemical Methods 155 

92. Chateau's Methods 157 

93. Reagents and Their Preparation 157 

94. Reactions of the Oils 158 

95. Use of Tabulated Reactions 164 

96. Alterations of Composition 179 

97. Action of Oils on Metals 1 79 

98. Impurities in Mineral Oils 182 

99. Density of Oils — Oleometers 184 

100. Baume's Scale and Specific Gravity 185 

101. Densities of Commercial Oils 187 



X CONTENTS. 

ART. PAGE 

102. Viscosity of Oils 189 

103. Gumming and Drying 192 

104. Nasmyth's Apparatus — Bailey's 194 

105. Effect of Heat on Lubricants 196 

106. Fire Tests 198 

107. Cold Tests — Congelation 200 

108. Heat Tests with Acids 201 

109. Oleography , 202 

no. Forms of Cohesion-Figures 204 

in. Tests of Oils by Electricity 205 

112. Machines for Testing Lubricants 205 

CHAPTER VI. 

EXPERIMENTS ON FRICTION — TESTING-MACHINES. 

113. Early Experiments 208 

114. Rolling Friction — Carriages 208 

115. Resistance of Railway Trains 211 

116. Rennie's Experiments on Friction of Solids 215 

117. Friction of Brakes and on Rails — Riveting 216 

118. Friction of Belts and Gearing 220 

119. Friction of Pump Pistons — Slides and Valves 224 

120. Fluid Friction — Semi fluids 225 

121. Friction of Gases 226 

122. Friction of Liquids 227 

123. Friction of Earth 231 

124. Mixed Friction 233 

125. Friction of Lubricated Surfaces — Morin 233 

126. Friction of Journals — Worm Gearing 235 

127. Size of Journals — Maximum Pressure 239 

128. Machines for Testing Lubricants — Early Forms and Tests 243 

129. The Ashcroft, the Woodbury, and the Riehle Machines 247 

130. Thurston's Testing Machine and Method of Operation 253 

131. Lux's Improvement 266 

132. Illustration of Method, Record, and Report on Tests 266 

CHAPTER VII. 

LUBRICATED SURFACES — COEFFICIENTS OF FRICTION — MODIFYING 

CONDITIONS. 

133. Variations of Friction of Lubricated Surfaces 274 

134. Commercial Oils under Moderate Pressures , 277 

135. Relative Standing of the Lubricants 280 

136. Relative Endurance of the Principal Oils t . . , 284 



CONTENTS. XI 

ART. PAGE 

137. Friction and Pressure 296 

138. Law of Variation of Friction with Pressure 298 

139. Velocity and Friction . . . 305 

140. Rest and Motion 315 

141. Friction as affected by Temperature 319 

142. Law of Variation of Friction with Temperature 322 

143. Later Researches 332 

144. Fluid Pressure between Journals and Bearings 339 

145. Production of Specified Quality of Oil — Conclusions 340 



CHAPTER VIII. 

THE FINANCE OF LOST WORK OF FRICTION. 

146. Conditions affecting the Value of Lubricants and Cost of Lost WorK . 343 

147. Defects of the Usual Methods of Valuation of Oils 347 

148. Outline of an Exact Method 347 

149. Development of the Analytical System 347 

150. Data required in its Application 351 

151. Units of Measurement 352 

152. Values of Quantities involved.. 353 

153. Illustrations of Application 355 

154. Conclusions 358 



FRICTION AND LOST WORK 



CHAPTER I. 
THEORY OF MACHINERY— ITS ACTION AND ITS EFFICIENCY. 

1. The Object of all Mechanism is to produce a certain 
definite motion of some part or parts — the position and form 
and the methods of connection of which are known and fixed — 
against any resistance that may be met with in the course of 
such movement. This operation is also usually effected by 
utilizing the action of some other piece of mechanism which is 
itself a " prime mover," or is driven directly or indirectly by a 
prime mover, such as a steam-engine or a water-wheel. Every 
machine and every train of mechanism is therefore a contriv- 
ance by means of which energy or power available at one 
point, usually in definite amount and acting in a definite direc- 
tion and with definite velocity, is transferred to other points, 
there to do work of definite amount, and there to overcome 
known resistances with known velocities. 

The object of the engineer in designing mechanism is to 
effect this transfer of energy and these transformations at the 
least cost and with least running expense, and hence with 
maximum efficiency of apparatus. It is often important to 
secure minimum volume and weight of machine, as well as 
maximum effectiveness in operation. 

2. The Work of a Machine is measured by the magni- 
tude of the resistance encountered and the velocity with which 
it is overcome. The nature of the work, aside from its simple 
kinetic character, is as widely variable as are the details of 
human industry. 



2 FRICTION AND LOST WORK. 

Prime Movers are those machines which receive energy 
directly from natural sources, and transmit it to other machines 
which are fitted for doing the various kinds of useful work. 
Thus, the steam-engine derives its power from the heat-energy 
liberated by the combustion of fuel ; water-wheels utilize the 
energy of flowing streams ; windmills render available the power 
of currents of air ; the voltaic battery develops the energy of 
chemical action in its cells ; and, through the movement of 
electro-dynamic mechanism, this energy is communicated to 
other machinery, and thus caused to do work. 

Machinery of Transmission is used in the transformation 
of energy supplied by the prime mover into available form, 
for the performance of special kinds of work, or for simple 
transmission of power from the prime mover to machines doing 
that work. 

The work to be done may be the raising of weights, as in 
hoisting and pumping machinery ; the transportation of loads, 
as on the railway or in the steamship ; the alteration of the 
form of solid masses, as in machine-tools ; the overcoming or 
even the utilizing of frictional resistances, as in brakes ; or any 
other of the numberless operations performed in mills and 
factories by machinery. 

Machines and Machine-tools receive energy, derived originally 
from prime movers, and transferred to them through machinery 
of transmission, and apply that energy to special kinds of work 
to which they are precisely adapted by their design and con- 
struction. Thus, looms apply such energy to the weaving of 
cloth ; lathes are especially fitted for the production of parts 
having circular sections ; planing-machines produce straight- 
lined surfaces. 

3. The Power demanded by a Machine is that needed to 
do the work for which the machine is designed, plus the addi- 
tional amount expended by the machine itself, in transferring 
the first-mentioned quantity from the source of power to which 
the machine is connected, by transmitting mechanism to the 
point at which the work is to be done. Where the machine is 
subject to shock and jar sufficient to permanently distort its 
parts, or the bearing surfaces, a portion of the power demanded 



THEORY OF MACHINES. 3 

is wasted in doing this work ; where the journals heat, consider- 
able amounts of energy are sometimes lost as heat-energy: in 
all cases some loss occurs in this way. Where power is trans- 
mitted by the expansion and compression of elastic fluids, also, 
energy is often lost in large amounts by transformation into 
heat. 

The power demanded by any machine thus always exceeds 
that expended by the machine upon its proposed task. Were 
these wastes not to occur, the power transmitted would be the 
same in amount at every point in the machine. 

4. Work, as a term in the science of engineering, may be 
defined as that action by which motion is produced against the 
resistance continuously or intermittently opposed to any mov- 
ing body. It is measured by the product of the direct com- 
ponent of the resistance into the space traversed. Where the 
resistance is variable, its mean value is taken. Thus, if R be 
the resistance and 5 the space, the work is, for constant 
resistance, 

U=RS, (1) 

in which U is measured in foot-pounds or kilogrammetres. 
For a variable resistance, R, acting through a space, s, 



U 



= fRds, (2) 



which can be integrated when R is known as a function of s. 

Resistances, and the forces by which they are overcome, 
are measured by engineers, usually, either in British or in 
metric units, as the pound or the kilogramme. Work, and the 
energy expended in doing work, are thus both measured by 
the product of the pounds or the kilogrammes of resistance 
or of effort into spaces of which the measure is usually given 
in feet or in metres. The unit of work and of energy is thus 
either the foot-pound or the kilogrammetre. 

The British and metric measures have definite relations, 
which are given in tables to be found in all engineers' table- 
books. 



4 FRICTION AND LOST WORK. 

Where the motion of the machine or of the part doing work 
is circular, the space traversed may be measured by the angu- 
lar motion, a> multiplied by the lever-arm, /, and their pro- 
duct, multiplied by the force, R, exerted, gives the measure 
of the work done. Thus : 

U =« Rl i (3) 

in which last expression n is the number of revolutions made 
in the unit of time. 

These values are equivalent to the product of the angular 
motion into the moment of the resistance. 

Work may also be measured, as in steam, air, gas, or water- 
pressure engines, by the product of the area of piston, A, the 
mean intensity of pressure upon it,/, the length of stroke of 
piston, /, and the number of strokes made. Thus, 

U—Apln 

= Aps 

=tr, ( 4 ) 

when Fis the volume of the working cylinder multiplied by 
the number of strokes ; in other words, the volume traversed 
by the piston. 

Where the force acting, or the resistance, acts obliquely to 
the path traversed, it is evident that only the component in 
that path is to be considered. 

Diagrams exhibiting the amount of work done and the 
method of its variation are often found useful. In such 
diagrams the ordinate is usually made proportional to the 
force acting or to the resistance, while the abscissas are made 
to measure the space traversed. The curve then exhibits the 
relations of these two quantities, and the enclosed area is a 
measure of the work performed. With a constant resistance, 
the figure is rectilinear and a parallelogram ; with variable 
velocities and resistances, it has a form characteristic of the 
methods of operation of the part or of the machine the action of 



THEORY OF MACHINES. 5 

which it illustrates. In the first case, the area can be obtained 
by multiplication of the difference of the ordinates by the 
difference between maximum and minimum abscissas; in the 
second case, it may be obtained by any convenient system of 
integration, of which systems that of mechanical integration, 
as by the " planimeter," is usually best. 

5. Power is defined as the rate of work, and is measured 
by the quantity of work performed in the unit of time, as in 
foot-pounds or in kilogrammetres, per minute or per second. 
The unit commonly employed by engineers is the " horse- 
power," which was defined by Watt as 33,000 foot-pounds per 
minute, equivalent to 550 per second, or 1,980,000 foot-pounds 
per hour. This is considered to be very nearly the amount of 
work performed by the very heavy draught-horses of Great 
Britain ; but it considerably exceeds the power of the average 
dray-horse of that and other countries, for which 25,000 foot- 
pounds may be taken as a good average amount. 

The metric horse-power, called by the French the dieval- 
vapear, or force de cheval, is about i-J- per cent less than the 
British, being 542-J foot-pounds or 75 kilogrammetres per 
second, 4500 kilogrammetres per minute, or 270,000 per hour. 
These quantities are almost invariably employed to measure 
the power expended and work done by machines. 

It is evident that power is also measured by the product of 
the resistance, or of the effort exerted into the velocity of the 
motion with which that resistance is overcome, or that force 
exerted. Since s = vt, 

U = Rs = Rvt] 

and when t becomes unity, the measure of the power, or of 
the equivalent work done in the unit of time, is 

U f = Rv, (5) 

in which the terms are given in units of force and space as 
above. 

The power of a prime mover is usually ascertained by experi- 
mentally determining the work done in a given time, the trial 



6 FRICTION AND LOST WORK. 

usually extending over some hours, and often several days. 
It is measured in foot-pounds or kilogrammetres ; the total 
work so measured is then divided by the time of operation 
and by the value of the horse-power for the assumed unit of 
time and the mean value of the power expended thus finally 
expressed in horse-powers.* 

6. The Forces acting in machines are distinguished into 
driving and resisting forces. That component of the force, act- 
ing to produce motion in any part which lies in the line of motion 
only, is that which does the work; and this component is 
distinctively called the " Effort." Similarly, only that compo- 
nent of the resistance which lies in the line of motion is con- 
sidered in measuring the work of resistance. In either case, 
if the angle formed between the directions of the motion of 
the piece and of the driving or the resisting force be called a r 
the effort is 

P=Rcos a. . (6) 

The other component, acting at right angles to the path of 
the effort, is 

Q = R sin a, (j) 

and has no useful effect, but produces waste of power by in- 
troducing lateral pressures and consequent friction. 

7. Energy, which is defined as capacity for performing 
work, is either actual or potential. 

Actual or Kinetic Energy is the energy of an actually mov- 
ing body, and is measured by the work which it is capable of 
performing while being brought to rest, under the action of a 
retarding force ; this work is equal to the product of its weight, 

v 2 
W, into the height, h = — , through which it must fall under 

the action of gravity to acquire that velocity, v, with which it 
is at the instant moving ; i.e., 

E= U=WA= W— (8) 

2g ^ 

* Custom has not yet settled the proper form of the plural of this word; there 
is no reason why it should not follow the rule. 



THEORY OF MACHINES. 7 

A change of velocity v 1 to v 2 , causes a variation of actual 
energy, E 1 — E 2 , and can be effected only by the expenditure 
of an equal amount of work — 

E 1 -E,^U=W -'^^ = W(K - h,). . . (9) 

This form of energy appears in every moving part of eve-ry 
machine, and its variations often seriously affect the working 
of mechanism. 

The total actual energy of any system is the algebraic sum 
of the energies, at the instant, of all its parts ; i.e., 

E=2W^, (io) 

and when this energy is all reckoned as acquired or expended 
at any one point, as at the driving-point, the several parts 
having velocities, each n times that of the driving-point, which 
latter velocity is then v, the total energy becomes 

2 2 

E = 2JV— -• (ii) 

Actual energy is usually reckoned relatively to the earth ; 
but it must often be reckoned relatively to a given moving 
mass, in which case it measures the work which the moving 
body is capable of doing upon that mass, when brought by it 
to its own speed. 

Potential Energy is the capacity for doing work possessed 
by a body in virtue of its position, of its condition, or of its 
intrinsic properties. Thus, a weight suspended at a given 
height possesses the potential energy, in consequence of its 
position, E = Wh, and may do work to that amount while de- 
scending through the height, h, under the action of gravity. 
A bent bow or coiled spring has potential energy, which be- 
comes actual in the impulsion of the arrow or is expended in 
the work of the mechanism driven by the spring. A mass of 
gunpowder or other explosive has potential energy in virtue 



8 FRICTION AND LOST WORK. 

of the unstable equilibrium of the chemical forces affecting its 
molecules. Food has potential energy in proportion to the 
amount of vital and muscular energy derivable by its consump- 
tion and utilization in the human or animal system. These 
potential energies are not measured by the observed actual 
energies derived from these substances in any case, but are 
the maximum quantities possibly obtainable by any perfect 
system of development and utilization. In practical applica- 
tion, more or less waste is always to be anticipated. 

8. The Law of Persistence of Energy affirms that the to- 
tal energy, actual and potential, of the universe, or of any isolated 
system of bodies, is of invariable amount, and that all energy 
is thus indestructible, although capable of transformation into 
various forms of physical and chemical energy. 

Every instance of disappearance of actual energy involves 
the performance of work, and the production of potential or 
of some new form of actual energy in precisely equal amount. 
A stone thrown vertically upward loses kinetic energy as it 
rises in precisely the amount — resistance of the air being ne- 
glected — by which it gains potential energy. A falling mass 
striking the earth surrenders the actual energy acquired by 
loss of potential energy during its fall, and the equivalent of 
the quantity so surrendered is found in the work done upon the 
soil ; it finally passes away as the equivalent energy of heat- 
motion produced by friction and impact. The potential chem- 
ical energy of the explosive is the equivalent of the kinetic 
energy of the flying projectile, and the latter has its equivalent 
in the work done at the instant of striking and coming to rest, 
and in the heat produced by the final change of mass-motion 
into molecular or heat motion. 

Energy in all its many forms is thus transferable in defi- 
nite quantivalent proportions, and in all cases changes form 
when work is done. Work may therefore be defined as that 
operation which results in a change in the method of manifes- 
tation of energy, and Energy as that which is transferred or 
transformed, when work is done. The motion of a projectile 
is the transfer of energy from one place to another. It is 
generated at the point of departure, stored as actual or 



THEORY OF MACHINES. 9 

kinetic energy, transferred to the point of destination, and 
there restored and applied to the production of work. 

9. Acceleration and Retardation of masses in motion can 
only be produced by doing work upon them, or by causing 
them to do work, and thus, by the communication of energy 
to them or by its absorption from them, in precisely the amount 
which measures the variation of their actual energy as so pro- 
duced. Every body which is increasing in velocity of motion 
thus receives and stores energy ; every mass undergoing re- 
tardation must perform work, and thus must restore energy 
previously communicated to it. In every machine which works 
continuously, and in which parts are alternately accelerated and 
retarded, energy is stored at one period and restored at 
another, in precisely equal amounts. 

Work done upon any machine may thus be expended partly 
in doing the useful work of the system, and partly in storing 
energy ; and the same machine may do work at another instant 
partly by expending the energy received by it, and partly by 
expending stored energy previously accumulated. 

10. Storage or Restoration of Energy thus always oc- 
curs when change of speed takes place. It is evident, since 
the storage or restoration of energy implies variation of speed, 
that the condition of uniform speed is that the work done upon 
the machine shall at each instant be precisely equal to that 
done by it upon other bodies. The work applied must be 
equal to that of resistance met at the driving-point. Thus, 

2Pv = 2Ri/] f Pdv =fRdv'; . . . (12) 

and the effort at each point in the machine will be equal to 
the resistance, and inversely as the velocity of the point to 
which it is applied; i.e., 

P v' , . 

R = V (I3) 

In the starting of every machine energy is stored during 
the whole period of acceleration up to maximum speed, and 
this energy is restored and expended while the machine is 



IO FRICTION AND LOST WORK. 

coming to rest again. This latter quantity of energy is usually 
expended in overcoming friction. 

11. The Useful and the Lost Work of a machine are, to- 
gether, equal to the total amount of energy expended upon the 
machine, i.e., to the work done upon it by its "driver." The 
Useful Work is that which the machine is designed to perform ;. 
the Lost Work is that which is absorbed by the friction and 
other prejudicial resistances of the mechanism, and which thus 
waste energy which might otherwise be usefully applied. 
These two quantities, together, constitute the Total Work or 
the Gross Work of a machine, or of a train of mechanism. In 
every case some energy is wasted, and the work done by the 
machine is by that amount less than the work performed in 
driving it. In badly proportioned machines the lost work is 
often partly expended in the deformation and destruction of 
the members of the construction ; in well designed and properly 
worked machinery loss occurs wholly through friction. In 
machines acting upon fluids this lost work is usually partly 
wasted in the production of fluid friction — i.e., of currents and 
eddies ; thus producing new forms of actual energy in ways 
which are not advantageous : even this waste energy is finally 
converted, like the preceding form, by molecular friction into 
heat, and is dissipated in that form of molecular energy. Thus 
all wasted work is lost by conversion from the energy of mass- 
motion into molecular energy and ultimately disappears as heat. 

12. The Efficiency of Mechanism is measured by the 
quantity obtained by dividing the amount of useful work per- 
formed by the gross work of the piece or of the system. It 
is always, therefore, a fraction, and is less than unity ; which 
latter quantity constitutes a limit which may be approached 
more and more nearly as the wastes of energy and work are 
reduced, but can never be quite reached. If the mean useful 
resistance be R, and the space through which it is overcome 
be /, and if the mean effort driving the machine be P, and the 
space through which it acts be s, the total and the net or 
useful work will be, respectively, Ps, Rs'; the lost work will be 

Ps — Rs' and the 

Rs f 

Efficiency = p- < i (14) 



THEORY OF MACHINES. II 

Counter -efficiency, C, is the reciprocal of the efficiency ; i.e., 

r Ps t x 

C =Rs < I5 > 

The efficiency and the counter-efficiency of a machine, or 
of any train of mechanism, is the product of the efficiencies or 
of the counter-efficiencies of the several elements constituting 
the train transmitting energy from the point at which it is 
received to that at which the work is done, i.e., from the 
" driving" to the " working" point. 

Friction is thus the principal cause, and usually the only 
cause, of loss of energy and waste of work in machinery. A 
given amount of energy being expended upon the driving- 
point in any machine, that amount will, in accordance with 
the principle of the persistence of energy, be transmitted from 
piece to piece, from element to element, of the machine or 
train of mechanism, without diminution, if no permanent dis- 
tortion takes place and no friction occurs between the several 
elements of the train, or between those parts and the frame 
or adjacent objects. Temporary distortion, within the limit 
of perfect elasticity, causes no waste of energy ; permanent 
distortion, however, causes a loss of energy equal to the total 
work performed in producing it. But permanent distortion is 
due to deficiency of strength and defective elasticity, and is 
never permitted in well-designed machinery properly operated ; 
and hence the important principle : 

The only cause of lost work in mechanism, which is to be 
anticipated in design and calculated upon in deducing the 
theory of special mechanism, is the friction necessarily conse- 
quent upon the relative motion of parts in contact and under 
pressure. 

The study of the laws of friction, the construction of its 
theory, and the experimental investigation of the conditions 
which determine the loss of efficiency in machinery by friction, 
are thus obviously of supreme importance to the engineer 
who designs, the mechanic who constructs, and the operator 
or manufacturer who makes use of machinery. 



12 FRICTION AND LOST WORK. 

In engineering, therefore, the principles of pure median, 
ism, of theoretical mechanics, and of pure theory in the science 
of energetics, or of thermodynamics, are to be studied as intro- 
ductory to a science of application in which all actions and all 
calculations are to be considered with reference to the modi- 
fications produced by the wastes of energy and the alteration 
of the magnitudes and other properties of forces consequent i 
upon the occurrence of friction. This is to the engineer a 
vitally important branch of applied science, and it is coexten- 
sive with the applications of mechanical science. 

13. The Magnitude of the Lost Work in machinery and 
mill-work is variable, but is always very large. It may prob- 
ably be fairly estimated that one half the power expended in 
the average case, whether in mill or workshop, is wasted in 
lost work, being consumed in overcoming the friction of lubri- 
cated surfaces. That this is true, is evident from the fact that 
the power demanded to drive the machinery of such establish- 
ments has been found by Cornut and others to be variable to 
the extent of 15 or 20 per cent by simple change of tempera- 
ture indoors from summer to winter, and a reduction of 50 
per cent in the work lost by friction has often been secured 
by change of lubricant. Mr. Fairbairn has found a change to 
the extent of 10 to 15 horse-power in a cotton-mill from the 
former cause. 

The friction of shafting in mills varies, with size and load- 
ing, from 0.33 to 1.5 horse-power per 100 feet (31 m.) length, 
averaging for the " main line," with good lubrication, about 
1 horse-power. The loss of power in mills ranges, with differ- 
ent machines, from 5 to 90 per cent, averaging for cotton and 
flax mills about 60 per cent, with good management, and in 
woollen mills about 40 per cent, the efficiencies being there- 
fore about 40 and 60 per cent for the two cases. The friction 
of heavy iron-working tools maybe taken at about /"= 0.15, 
the efficiency at 0.85. The loss in the steam-engine is usually 
nearly constant at all powers, and ranges from 4 pounds per 
square inch (0.27 atmosphere) on small engines of 25 to 50 
horse-power, down to 1 pound (0.07 atmosphere) in very large 
marine-engines: this gives efficiencies ranging from 0.84 to 95 



THEORY OF MACHINES. 1 3 

or 97 per cent. In a " high-speed " engine intended to drive 
electric lights the author found the efficiency to be 

T?rn • O.06 

Efficiency =1 ==-, 

in which U is the work done, calling work " at full stroke" 
unity. Rules for calculating the magnitude of this loss will 
be given in later chapters. 



CHAPTER II. 

NATURE AND THEORY OF FRICTION. 

14. Friction is that familiar resisting force which always 
acts to prevent or to retard the relative motion of one par- 
ticle or body in forced contact with another. It is of three 
kinds : sliding and rolling friction, acting between solids ; and 
fluid friction, which acts when the particles of liquids or of 
eases move in contact with each other or with other bodies. 
These three kinds of friction are different in character, and are 
governed by quite different laws ; these laws also are in many 
cases quite different from those usually given in earlier works 
on this subject. 

Friction acts at the surfaces of contact of the two particles 
or masses between which it is exhibited, and in the direction 
of their common tangent, resisting relative motion, in which- 
ever direction it may be attempted to produce it. Friction is 
thus always a resisting force, and never of itself produces or 
accelerates motion. It may act usefully in increasing the sta- 
bility of structures, or injuriously by resisting the motion of 
mechanisms, and by producing waste of power and work ; it 
may also be utilized in the absorption of surplus energy, or in 
the transmission of motion from one to another of movable 
parts in contact. 

In any simple machine or in any train of mechanism, if 
either be absolutely rigid or absolutely elastic, — i.e., not sub- 
ject to deformation, — the only losses of energy are those pro- 
duced by friction. This important principle has the important 
corollary, that the " efficiency" of a machine is known when all 
its frictions are determinable. 

Friction of motion, whatever the kind considered and 
whatever its cause, always results in the conversion of an 



THEORY OF FRICTION. I 5 

amount of energy, measured by the work of friction, into heat. 
In accordance with the law of the " persistence of energy," and 
with the " first law of thermodynamics," this production of 
heat occurs, in every case, in the proportion of one British 
thermal unit for each 772 foot-pounds of work absorbed by 
friction, or of one metric heat-unit for each 423.55 kilogram- 
metres of energy so lost. The amount of heat produced may 
therefore be calculated by dividing the total work of friction, 
for any given case, by this "mechanical equivalent of heat." 
Thus one horse-power expended in friction results in the con- 
version of work or energy into 

M^ = 43 «B.T.U.," 
772 

(British thermal units,) per minute; 10 chevaux de vapeur 
similarly expended in overcoming friction, produce 

■ =1.8 Calories. 

423-55 

(metric thermal units,) per second, or 108 per minute nearly. 

15. Moving and Resisting Forces are met with in all 
mechanical processes. The former are those which are active, 
and produce or tend to produce change of motion in bodies ; 
the latter are those which are purely passive, and only resist the 
action of forces of the first class. Gravity, heat-energy, and 
all other energies, including that of muscular force, illustrate 
the first, and friction is of the second, class. Moving forces 
may either produce or destroy motion ; but resisting forces 
can only resist and reduce motion. Forces of the first class 
are definite, and may be entirely independent of the forces by 
which they are opposed or aided ; those of the second class 
are indefinite indirection, and, within limits, in magnitude, and 
are variable with the magnitude, direction, and point of appli- 
cation of the moving forces which they oppose. Moving 
forces are evidently in their nature determinate; resisting 
forces are as obviously in their nature indeterminate. 



1 6 FRICTION AND LOST WORK. 

Friction is evidently of this latter class ; and the Force of 
Friction has a variable magnitude, from o to its maximum, 
f JV, with variation of the active force which it may resist. 

16. The Friction of Solids is caused by the roughness 
and unevenness of the surfaces of contact. In the case of 
Sliding Friction the asperities of the one surface interlock with 
those of the other, and motion can only take place by the rid- 
ing of the one set over the other, by the tearing off of the 
projecting parts, or by rubbing them down : in either case the 
process gives rise to a resistance which is the greater as the 
roughness is greater, and the less as the surfaces are smoother ; 
an absolutely smooth surface would be frictionless. Rolling 
Friction is observed where any surface of revolution, or other 
smoothly curved surface, is rolled upon another surface, plane 
or curved. Its cause is identical with that of sliding friction, 
that irregularity of form and of surface which will not permit 
motion to occur without irregular variation of the distance 
between the centre of gravity of the rolling body and the line 
of motion in the common tangent of the two bodies, at the 
point or line of contact. Where the surfaces are hard, smooth, 
and symmetrically formed, this friction is small ; where they 
are soft, rough, or irregular, this form of friction is observed 
in greater degree, Absolutely smooth, hard spheres or cylin- 
ders, rolling on absolutely hard, smooth surfaces, meet with 
no frictional resistance ; bodies having rough surfaces, those 
made of compressible material, and those of irregular surface 
and form, exhibit greater friction as these defects are exag- 
gerated. Both forms of resistance evidently depend upon the 
character of the material as well as upon the form of the sur- 
faces of contact. 

The resistance of knife-edges, as in balances, is a form of 
rolling friction. 

17. The Laws of Sliding Friction, with solid, unlubricated 
surfaces, are, up the point of abrasion, as follows : 

(1) The direction of frictional resisting forces is in the 
common tangent plane of the two surfaces, and directly 
opposed to their relative motion. 



THEORY OF FRICTION. 1 7 

(2) The point or surface of application of this resistance is 
the point or the surface on which contact occurs. 

(3) The greatest magnitude of this resisting force is 
dependent on the character of the surfaces, and is directly pro- 
portional to the force with which the two surfaces are pressed 
together. 

(4) The maximum frictional resistance is independent of 
the area of contact, the velocity of rubbing, or any other 
conditions than intensity of pressure and condition of the 
surfaces. 

(5) The friction of rest or quiescence, " statical friction," 
is greater than that of motion, or " kinetic friction." 

These " laws" are not absolutely exact, as here stated, so 
far as they affect the magnitude of friction-resistance. 

It is found that the resistance to sliding of " skidding" 
wheels on railways is less as speed is greater; but it is not 
known to what extent this is due to the separation by jarring 
of wheel and truck. It is also found that some evidence exists 
indicating the continuous nature of the friction of rest and 
motion. 

When the pressure exceeds a certain amount, fixed for each 
pair of surfaces, abrasion of the softer surface or other change 
of form takes place ; the resistance becomes greater, and is no 
longer wholly frictional. When the pressure falls below a 
certain other and lower limit the resistance may be principally 
due to adhesion, an entirely different force, which may enter 
into the total resistance at all pressures, but which does not 
always appreciably modify the law at higher pressures. This 
limitation is seldom observable with solid, unlubricated sur- 
faces, but may often be observed with lubricated surfaces, the 
friction of which, as will be presently seen, follows different 
laws. The upper limit should never be approached in 
machinery, but is often reached in framed structures. 

18. The Coefficient of Friction is that quantity which, 
being multiplied by the total pressure acting normally to the 
surfaces in contact, will give the measure of the maximum 
frictional resistance to motion. It follows from the third law 



18 



FRICTION AND LOST WORK, 



above stated (Art. 17), that the greatest force with which rela- 
tive motion is resisted by friction is obtained by thus multiply- 
ing this total pressure by a constant coefficient to be determined 
experimentally for every pair of surfaces of definite character. 
Thus, if N represent the normal force binding the one surface 
to the other, if F be the maximum resistance due to friction, 
and if /be the coefficient of friction, 



F = fN; f 



F^ 

N' 



The value of f being determined by experiment, it is con- 
stant, within the limit already stated, for all pressures occurring 
between the given surfaces. As will be seen later, its value is 
variable for lubricated surfaces with variations of velocity, of 
intensity of pressure, of temperature, and probably with other 
conditions. 

19. The Methods of determining Coefficients of Friction 
are usually very simple. Where a heavy body, W (Fig. 1), 




Fig. 1. — Sliding Friction. 



slides upon a plane, AB, the magnitude of the force, F, 
required to cause motion, or to continue motion once started, 
can be determined by carrying a cord over a pulley, C, and, 
one end being attached to the mass to be moved, and the 
other being loaded with such a weight, F t as is needed to cause 
motion or to keep up a given velocity of sliding, the value of 
the coefficient, f, becomes known, and we have 



/= 



F_ 
W 



THEORY OF FRICTION. 



19 



The force F may often be most conveniently measured by a 
spring balance attached to a cord pulling in the line of motion 
of W. 

An equally easy method of ascertaining the value of f is 
illustrated in Fig. 2. An inclined plane AB, of variable angle 




Fig. 2. — Sliding Friction. 

of inclination, a, is constructed of one of the materials between 
which the friction is to be determined ; while a body of any 
convenient size, and of the same or other material, as may be 
desired, is placed upon the inclined surface. To determine the 
coefficient of friction for rest, the plane is raised to such an 
angle, a, that the body will just start down the plane without 
the application of an external impelling force. At this instant 
the friction is due to the pressure produced by that component, 
CD, of the weight which produces the normal pressure, and 
which is equal to the reaction, R, of the surface against the 
sliding body ; it is measured by 

fR=fWcos a, 

as well as by that component of the total weight, W, acting 
along the plane to cause sliding. Hence 



fR=/Wcosa= Wsina; 

sin a 

f= =tan a ; 

J cos a 



and the value of the coefficient of friction is equal to the 



20 FRICTION AND LOST WORK. 

tangent of the inclination of the plane. Otherwise, resolving 
parallel and perpendicular to the plane, we have 

fR — Wsm a — o, 
R — IV cos a = o ; 

then, eliminating R and W, we have 

fcos a — sin a = o, 
or, as before, /= tan a. 

The angle a is often called the angle of friction, or the 
limiting angle of resistance, and is usually designated by the 
letter <p. 

Various other methods are used, some of which will be 
described in later chapters, in which accounts of experimental 
work will be given. 

The coefficient of friction,/", is by many writers denoted by 
the letter //. 

20. Angle of Friction ; Cone of Resistance.— The total 
action of any surface upon a body moving in contact with it 
is the resultant of two components, one of which is the reac- 
tion, R, in a line normal to the surface, and the other of which 
is the resisting force of friction, F, equal and opposite to the 
effort tending to produce motion along the surface ; these two 
forces are therefore at right angles to each other, and their 
resultant is 



9 = VR* + F\ 

and its direction may be such as to make any angle with the 
tangent and the surface greater than o, or less than q> =t tan f 
Exceeding the latter limit, accelerated motion takes place. 

The movable body will evidently remain at rest, whatever 
the direction of this resultant force, provided its direction 
does not fall outside a cone of which the apex is at the point 
of application of the resultant force, and of which the semi- 
angle is = tan - x f. This Angle of Friction, q>, thus deter- 



THEORY OF FRICTION. 21 

mines the Cone of Friction, as it is usually called ; which cone 
is generated by causing the line defining the angle of friction 
to revolve about the normal : this cone thus embraces the 
direction of all possible forces which do not produce motion. 
When the cone of friction is referred to without qualification, 
the friction implied is usually statical friction — the friction of 
rest. 

It follows from what has preceded, that the stability of a 
system composed of a pair of bodies in contact is determined 
by the angle of friction and the location and the form of the 
cone of friction, and that the greatest angle of obliquity of 
the resultant pressure in a stable system is the angle of which 
the tangent is equal to the coefficient of friction ; this is the 
angle of repose, cp. For cases of equilibrium, the force of fric- 
tion is fN= iVtan cp = W sin cp, where IV and N are respec- 
tively the applied force and its normal component. 

21. The Friction of Rest, or Statical Friction, although 
in the case of the sliding of solids precisely of the same nature 
as the friction of motion or dynamical friction, is often of very 
different magnitude and sometimes follows different laws: the 
former is always greater than the latter, and where the pres- 
sure is of great intensity is frequently enormously greater than 
when the relative velocity of the rubbing surfaces is consider- 
able. The friction of rest is also often increased, especially 
where one or both of the surfaces is of soft material, by time 
of contact. This apparently comes of the fact that the two 
surfaces when left under pressure, imbed themselves, the one 
in the other, more and more thoroughly as time passes, until 
in some instances adhesion occurs, and the frictional resistance 
to starting them apart is reenforced by molecular forces. 
With hard bodies and with light pressures these differences 
are less observable, and are often unimportant. 

The magnitude of the coefficient of friction for rest is very 
variable, but usually increases with increasing pressures; its 
value for special cases will be given in a later chapter. 

22. The Friction of Motion, or Kinetic Friction, only 
differs from statical friction in its magnitude. It is always 
less between any given pair of surfaces and under any given 



22 FRICTION AND LOST WORK. 

pressure than statical friction, with the conditions, other than 
the difference as to motion, the same. The value of its 
coefficient is less as velocity increases from zero, passes usually 
if not in all cases a minimum, and then increases again ; it 
becomes less as pressure increases, up to a limit also, passing 
which it again increases until abrasion occurs. 

With lubricated surfaces these differences become more 
observable than with dry surfaces, and the methods of variation, 
as will be seen later, often differ greatly. 

The direction of either form of the Force of Friction is 
always, as has been seen, directly opposed to the direction of 
motion, or of the resultant forces attempting to produce 
motion ; and its magnitude is always just sufficient to equili- 
brate the resultant moving force, up to a maximum which is 
reached when that force becomes equal to the maximum 
resistance, fN. 

23. The Differences between the two Frictions are 
evidently of such magnitude as to be of very great importance 
in construction. It is found that a jar, often a very slight one, 
will convert the friction of rest into the friction of motion, 
and, motion once commenced, it continues with acceleration 
of velocity until the total resistance equilibrates the resultant 
impelling effort. In machinery, therefore, it is often difficult 
to set the train in motion, but comparatively easy to sustain a 
velocity once acquired. A train on a railway may be started, 
the friction of rest being overcome by jar in one car after 
another, when loosely "coupled ;" while the same locomotive 
may be quite incapable of starting a train of the same size and 
kind, closely and rigidly coupled. Once in motion, the two 
trains are moved with equal ease. The greater the intensity 
of the pressure, the greater the difference in resistance, and 
the more difficult it is to convert the one form into the other. 
It is probable that the law of variation, so far as it relates to 
speeds of rubbing, is continuous, the coefficient insensibly 
changing as speed decreases to the value of rest, as the veloc- 
ity passes through insensibly small values to o. 

As the slightest jar will usually convert the friction of rest 
into friction of motion, no machinery subject to jar need be stud- 



THEORY OF FRICTION. 23 

ied with reference to the modification of its efficiency by the 
former kind of friction. In any system subject to jar, also, the 
parts normally at rest will gradually assume the positions which 
a similar system absolutely at rest would take if perfectly 
frictionless. This principle is very often of practical impor- 
tance. This does not reduce the lost work in a train of mov- 
ing machinery to zero, however, as work is expended in pro- 
ducing the jarring. 

Motion in one direction also reduces or may even elimi- 
nate the effect of friction in another direction. Thus, in the 
hydraulic testing-machine of Mr. C. E. Emery the rotation of 
the " ram" of the hydraulic press eliminates the effect of fric- 
tion in its longitudinal movement, and permits as exact meas- 
urement of the resistance of the test-piece as if the plunger or 
ram were frictionless. 

24. The Principle of Equilibrium, as it is termed, for cases 
in which it is attempted to move bodies against the force of 
friction is the following: 

Determine the reaction of the supporting surface under 
the actual or assumed conditions, by finding the resultant of 
all other forces acting upon the supported body ; then if the 
direction of this resultant falls within the cone of friction 
equilibrium will exist, the body will remain at rest, and the re- 
sistance of the surface is equal and directly opposed to this 
resultant. 

The single condition of equilibrium and rest is, therefore, that 
the applied forces should have a resultant lying within the cone 
of friction. The magnitude of the force of friction is deter- 
mined in such cases of equilibrium by resolution of the result- 
ant obtained, as above, into components parallel and perpendic- 
ular to the surface at its point of application, and measuring the 
parallel component, which is the force of friction. 

25. A Solid resting on any actual Surface, even if both 
are apparently ever so hard and smooth, will nevertheless 
always be connected with it by projecting and interlocking 
particles, which may be microscopic or less than microscopic in 
size, but which may offer appreciable resistance to motion. 
The two bodies being left in contact, their surfaces gradually 



24 



FRICTION AND LOST WORK. 



come into more and more intimate contact, bringing new sets of 
particles into connection, and imbedding the set first in contact 
more thoroughly, until a permanent condition is reached. The 
coefficient of friction and the force of friction then attain maxi- 
mum values, and offer greatest resistance to motion. At any 
given instant, if f represent the coefficient of friction, N the 
normal reaction of the surface, and a the angle made by the 
acting force, W> with the surface itself, the force of friction will 
be^TV, and the body will remain at rest so long as the compo- 
nent of the applied resultant force parallel with the surface is 
less than this quantity, fN = W sin a. 

In illustration of the theory of friction on planes, let it be 
required to determine the inclination, a, of a prismatic body, 
as a beam, AB (Fig. 3), resting at one end upon a horizontal 
surface, A C, and at the other end against a vertical surface, 
BC, when just in equilibrium and about to slide down. 

Let its length AB = /, I' = the distance of its centre of 
gravity from its foot, and let/" and f be the coefficients of fric- 
tion, for rest, on the horizontal and vertical surfaces respec- 
tively, and R and R! the reactions 
of those surfaces at the points of 
contact ; let W be the weight of 
the beam. 

Resolving, we have 
R! -fR = o y 
R+f'R>-W=o, 
W=R{i+ff), 
and R'= fR. 



Taking moments about A, 




Fig. 3. — Friction of Solids. 



W . I ' . cos a — R'. I . sin a — f'R '. I . cos a = O, 
W. I -f'R I 



tan a 



R'l 



tan = 



r-(i+ff)-iff' 






THEORY OF FRICTION. 



25 



If the centre of gravity of the beam is at the middle, /= 2/', 



and 



tan a = 



2f 



26. A Solid resting on an Inclined Plane, and acted 
upon by its own weight and by external forces, is the simplest 
and best illustration of the general case. 

The following proposition will illustrate the mathematical 
application of the principles of the theory of friction to this 
case : 

(1) To determine the limiting ratios of P to W, friction act- 
ing up or down the plane, AB (Fig. 4), when P represents the 
effort exerted on the sliding body, W is its weight, and R is 
the reaction of the plane, which makes an angle, a, with the 
horizontal. 

Let the force, P, make an angle, /?, with the surface of the 
plane, AB, the body moving up the plane. 




Fig. 4. — The Inclined Plane. 

Since there exists an equilibrium of forces, we shall have, for 
the maximum value of P, 

P cos /? —fR— PTsin a = o, 
P sin J3 -f- R — W cos a = o, 



whence 



__ ^(sin a -(-/cos a) 
cos P-\-f sin /3 



(1) 



26 FRICTION AND LOST WORK. 

For a minimum value, we get, when the body slides down,, 

P cos fi+fR— W sin a = o, 
Ps'm J3 -\- R — W cos a = o, 

and p= W(sma-/c OS a) _ _ •_ (2> 

cos j3 —fsm fi 

Motion cannot occur if the value of P falls within the two 
limits above deduced, if /be taken as the coefficient of friction 
for rest. If taken for motion, the velocity will be constant in 
the two cases taken, and accelerated for intermediate values of 
P, the body moving down the plane ; and retarded motion 
occurs if the body moves up the plane. 

(2) Making P = o, we have 

sin a — /cos a = o, 

/= tan a = tan q>, (3) 

as before, and the tangent of the angle of inclination of the 
plane measures the coefficient of friction for rest, if the body 
is in equilibrium without motion, or the coefficient for motion 
if the body slides with uniform velocity. 

(3) If the effort act in the surface of the plane, /3 = o, and 

P= W (sin a ± /cos a), (4) 

the positive sign being taken for a pull up the plane, and the 
negative for an effort acting down the plane. The difference is 

AP= 2/Wcosa. ....... (S) 

(4) Making / = 0, we have 

P • BC tf* 

W = sma ^AB> •••••• ( 6 > 

and the effort is to the weight of the body as the height of the 
plane is to its length. 



THEORY OF FRICTION. 

(5) When the effort is parallel with the base, ft = 
W(s'm a i/cos a) 



P = 



cos a =F/"sin a 



and when/= o, 



W 



= tan a 



BC 
AC 



27 
— a, and 

• • (7) 

• • (8) 



the effort being to the weight as the height of the plane is to 
the length of its base. 

(6) In the case of a prismatic body, as a beam (Fig. 5), 
resting on the curved surface of a cylinder, the weight that 
may be suspended at the end without causing it to slide may 
be determined readily by the application of the principles 
above given. 

. Let G be the centre of gravity of the 
beam AB (Fig. ), whose length is 2/, and 
BG = /, the beam being uniform, W= its 
weight, and W the weight suspended from 
the end B. Before the weight W was sus- 
pended from the beam the point G evident- 
ly was at C. Let C be the point of contact B 
with the cylinder, the beam being on the 
point of sliding off, a the angle it makes 
with the horizon, and r = the radius of 
the cylinder. 

Resolving parallel and perpendicular to 
the beam, we have 

fR — W sm a— W sin a= o, 
R—W cos a — W cos a = o ; 

/= tan a. 

Taking the moments about C, we have 

W . BC cos « — W . C'g . cos a = o, 

or W . {BG - A'g) - W. Cg= o. 




5. — Sliding 
tion. 



28 



But 



FRICTION AND LOST WORK. 

Cg = arc C'C — radius X angle COC — r.a. 



W'.{l-rd)- W.ra = o, 



and 



W= 



W. ra W. r tan ~ x f 
I— ra'~ l—r tan ~ l f 



the weight required. 



(7) Let the cylinder diminish in size until its diameter may 
be neglected ; and let the end of the beam, AB (Fig. 6), rest 
against a vertical wall at ft. Then the position of equilibrum 
is found thus: 

The forces now acting are, the 
weight of the beam, W; the pressure 
on the support, equal to the reac- 
tion, R ; and the pressure on the 
wall, equal to the reaction R' . W 
acts vertically downward, R per- 
pendicularly to the beam, and R' 
perpendicularly to the face of the 
wall. The half length, /, of the 
beam, and the distance, £70 = d, 
from the support to the wall are 
known, and the position of equilib- 
rium becomes known when the 
angle, a, between the beam and the 
perpendicular to the wall, or its com- 
plement, /?, the angle with the face of the wall, is known. 
We have, without friction, 

CO 

sin p v } 

and, resolving horizontally and vertically, 

R' — Rqos/3 = o; (2) 

W— R sin /3 = o. ...... (3) 




Fig. 6. — Sliding Friction. 



Also, taking moments about B, 

RBO - Wl sin /3 = o ; 
Rl- Wl sin 2 /?= o. 



(4) 
(5) 



THEORY OF FRICTION. 2g 

Then, combining equations, 

sin 3 /?=^; . (6) 

W 

R = ^j-< w 

R! = R cos fi = PTcotan /?, (8) 

which gives the values of all three unknown quantities, when 
the wall and support are smooth. 

Where friction enters, we have motion opposed by it, 
although no tendency to motion exists for the position just 
determined. If the rod be moved from this position, the end 
B being gradually carried downward, along the wall, the force 
of friction gradually increases, but no motion can occur from 
any of the successive positions until a certain limit is reached, 
when the tendency to slide is sufficient to overcome the fric- 
tional resistance and a new position of equilibrium is thus 
found. In this position a force of friction, fR', acts upward 
at B, and a force, fR, resists sliding at O, acting in the direc- 
tion, BO. 

The equations of equilibrium now become 

R'— fR sin — R cos /3 = o; .... (9) 
W-fR'-Rsm/3 = o; .... (10) 
Rdr Wts'm 2 {3 = o; 

and finally, eliminating R and R', 



I «... 



d 



si 



n 3 J3=f-r sin 2 /? (cos/?— /sin /?) ; . . (11) 



which will determine /?.* 

Finally, carrying the end of the beam upward, a similar 

*See Thomson and Tait ; Nat. Phil., vol. i., § 572. 



30 FRICTION AND LOST WORK. 

process will give the position of equilibrium when the frictions 
act in the opposite direction, and the equation becomes 

-^sin 3 /? — I =f-j sin 2 /?(cos/?+/ sm /?). . (12) 

(8) Suppose a rectangular block to lie upon a horizontal 
plane ; to determine whether it will slide or turn over, we 
have, known, the reaction of the plane, 

R= IV; . . . . . . . . (1) 

the resistance of friction, equal to the effort 

P = fR = fW; (2) 

and the moments of P and of W equal for the position of 
equilibrium, and if the half thickness of the block be t and the 
height of the point of application of the effort be h, 

Wt = Ph; . . . . . . . . (3) 

P = {W. ........ (4) 

Hence, if the maximum pull, P, is less than fW, i.e., if 



f>i • • • (5) 



the mass may be overturned. 

It is evident that the body will not turn if the resultant of 
the weight of the mass, and the maximum effort to move it, 
i.e., the maximum effort permitted by friction, pierces the sup- 
porting plane within the base of the prism. 



THEORY OF FRICTION. 



31 




Sliding Friction. 



(9) A heavy body, ABCD, is secured to two rings, FG, 
which may slide on a vertical post, HK, and is so formed or 
so loaded, that its centre of gravity K 
falls at a known point, E. 

The reaction of the point A must 
evidently take the direction AE ; that 
of D, the direction DE\ and the only 
other force, if no friction exists, is the 
weight of the mass, W, acting vertically 
through E. This system of forces is 
extended by the introduction of fric- 
tion to include a vertical force resisting 
sliding, acting upward at the rings; 
and the impelling effort will always be 
the difference between the newly intro- 
duced force and the weight. The mag- 
nitude of the force of friction is found 
by multiplying the horizontal components, R, R' t of the forces 
in FE, GE, by the coefficient of friction,/*; and it is evident 
that, by making the distances between the rings small enough, 
and the distance out to the centre of gravity of the mass great 
enough, we may always make 

f(R + K')> W, 

and thus secure conditions which prevent the descent of the 
body along the supporting post. 

27. Solids moving on rough Surfaces are subject to pre- 
cisely the same conditions at each instant that obtain where 
the body is simply at rest, and resisting an effort tending to 
produce motion. Kinetic friction differs, however, from stati- 
cal friction, as has been stated, in the fact that the force of 
friction is always the maximum obtainable with the existing 
value of the coefficient, while in the case of statical friction 
that is the maximum limit simply; they also differ in the fact 
that the coefficient for motion often varies from instant to 
instant, and the direction of the force must also constantly 
change if the direction of motion varies, the two directions 
being always directly opposed. 



32 FRICTION AND LOST WORK. 

When motion occurs against the force of friction, the effort 
required to overcome it is lessened the instant that motion 
begins, and may afterward increase or diminish according to 
circumstances, some of which will be described later. In all 
cases, since the resistance is overcome by a constantly exerted 
effort acting through measurable spaces, work is done in 
measurable amount, and an equivalent amount of mechanical 
energy is transformed in all cases into heat-energy. This 
occurs, as already stated, in the proportion of one British 
thermal unit to each 772 foot-pounds of work, or of one metric 
thermal unit for each 423.55 kilogrammetres. The work of 
friction is therefore a quantity of importance to the engineer 
for two reasons: if excessive in amount, it absorbs and wastes 
a seriously large amount of otherwise available and useful 
energy; it also converts all this energy into heat, which 
heat may give rise to inconvenience, injury of parts, or even 
destruction of the machine. Provisions must always be made, 
therefore, to reduce and to carry away this heat, if of consid- 
erable amount, in such a manner as to do no damage. This is 
often a problem of very serious importance, and not infre- 
quently is very difficult of solution. The work of friction is 
always measured by the quantity, fNs, in which f is the 
coefficient of friction, N is the normal pressure on the support- 
ing surface, and s is the distance traversed on that surface. 

The friction of motion, or kinetic friction, is less variable, 
where the same two surfaces are used, than the static form of 
friction ; but it is always different in amount under the same 
pressures. These differences ape exaggerated where lubrica- 
tion is resorted to. The coefficient of friction for motion may 
often remain nearly constant for a vastly wider range of pres- 
sure than that for rest, and the work done against friction is 
correspondingly uniform. 

The condition of equilibrium, the body being in a state 
bordering upon motion, is that the direction of the resultant 
pressure shall lie in the surface of the static cone of friction. 
The condition that the body shall start from its state of rest is 
that this pressure shall be directed in a line exterior to that 
cone. The condition of uniform motion is that the direction 



THEORY OF FRICTION. 



33 



of that pressure shall subsequently lie in the surface of the 
cone of friction defined by the coefficient of kinetic friction. 
The conditions of accelerated and of retarded motion are that 
the direction of pressure shall fall outside of or within the 
latter surface, as the case may be. A body starting into free 
motion, under the action of an effort just sufficient to overcome 
the friction of quiescence, will move with accelerated velocity,. 
the acceleration being proportional to the difference between 
the friction of rest and that of motion. Conversely, a body 
being in a state of equilibrium under the action of any set of 
forces, if the body be at rest, the line of direction of the resultant 
of all forces, other than the reaction of the supporting surface,, 
must be coincident with an element of the static cone of fric- 
tion ; if the body be in kinetic equilibrium, moving with uni- 
form velocity, the resultant effort must be coincident with an 
element of the cone of kinetic friction. 

Where a heavy piece (Fig. 8) slides upon a smooth plane, 
the simplest method of treatment is to combine the weight of 
the piece with the resistance, R, which is also known in magni- 
tude, direction, and point of application, and thus to determine 
a " given force," R', as defined by Rankine. The line of action 
of the effort, P, causing equi- 
librium or motion is known. 
Let the angle, a, be made by 
the " given force" with the 
surface of the plane ; let /3 be 
the angle made by the effort, 
or the " driving force," P, 
with the same plane, and call 
the coefficient of friction/". 

Then the total pressure 
on the plane is Fig. 8.— Sliding Friction. 




R r sin a + P sin fi = W (i) 



The friction is 



fW = f {R! sin a + P sin /J). . . . (2) 



34 FRICTION AND LOST WORK. 

The resistance to sliding is 

R cosa+fW = R' (cos a +/sin a) -f i/sin fi ; (3) 

= Pcosj3 (4) 

The work done against friction is 

fWs =fs(R'sina+Psm/3), .... (5) 



where 



p - R t cos a +f s ™ or) 

cos /? — /sin /J W 



Examples illustrating Kinetic Friction are constantly met 
with in machinery. Such cases will be taken in some detail 
in a later chapter, while this phenomenon as exhibited in the 
elementary parts may be treated here. 

In all cases, as previously stated, the action of friction in a 
machine results in the increase of the effort required to drive 
it, and hence in the compulsory enlargement and strengthen- 
ing of parts and of the frame of the machine ; it also causes 
a waste of energy measured by the total work of friction, 
and a reduction of the efficiency of the machine by the con- 
version of this work into heat-energy ; and hence it compels 
the application of greater power and the use of a larger and 
stronger machine than would be otherwise needed to do the 
given work. The following cases illustrate the more impor- 
tant principles involved in the working of mechanism subject 
to friction : 

(1) Let any body be moved along a surface on which it 
presses with its full weight, and for which the coefficient of 
friction is known, the surface having a varying inclination. 
Determine the work of friction. 

For a surface of varying inclination, a, and the effort acting 
in the surface, from the principle of equality of energy exerted 
and work performed, if ds is the space traversed and U the 
work, 

dU — Pds = W sin a ds -J- Wf cos a ds. . . (1) 



THEORY OF FRICTION. 35 

But for any small movement, if dh is the height and dl the 
horizontal distance traversed, 

d/i = ds . sin a ; dl = ds . cos a ; 
and 

Pds= W.dk+W.fdl; 

whence, integrating 

U=Ps= W(A+fi), (2) 

and the total work is the sum of the work done in raising the 
body through the height h = BC (Fig. 4), and in sliding the 
mass, against friction, through the space, / — AC; and it is 
in no way influenced by the form of the path from A to B. 

(2) The best value of the angle /3 is found by making the 
value of P a minimum, i.e., making cos fi-\-f sin /?, in equa- 
tion (1), § 26, a maximum ; and we have 

/cos /? — sin /? = o ; 

= tan-V; (3) 

whence it follows that ft should be equal to the angle of fric- 
tion and positive, the direction of P rising above that of the 
surface of the plane, making an angle at every instant with 
the tangent plane to the surface, at the point of contact, equal 
to the kinetic angle of friction. 

(3) A body moving in any known path and with any given 
initial energy, ^MV" 1 = Wh = U, being retarded by friction, it is 
easy to determine the space through which it will move be- 
fore expending its energy and coming to rest. 

For from the law of equivalence of energy expended and 
work performed, 

\MV % = Wh =fNs = U; (4) 

and hence 

S 2fN ~ ~fN fN y 






$6 FRICTION AND LOST WORK. 

and the space may be found by dividing the initial energy by 
the mean value of the product of the coefficient of friction, f, 
into the normal pressure, N, at the point of contact between 
the two bodies. 

This is true for all possible cases. Thus a heavy body 
thrown along the surface of smooth ice moves farther than on 
a surface of wood, the initial velocity being the same, because 
the force of friction is less and the distance traversed in doing 
the same work is correspondingly greater. A fly-wheel, revolv- 
ing on its shaft-journals, if unacted upon by external forces, 
turns until the work of friction in the journals and in the air 
in contact with it is sufficient to abstract all its initial energy 
of rotation; and, neglecting the effect of the resistance of the 
air, the product of the pressure on the journals into the mean 
coefficient of friction, being multiplied by the velocity of rub- 
bing of the journal-surface and by the time, the product is the 
work so done, and is equal to the total initial energy of the 
wheel. 

(4) A Taper Key, such as is used in machinery, illustrates 
a common application of the principles controlling friction of 
moving bodies on inclined planes. If the half-angle of the 
" taper" of the key is ex, the effort required to start it is pro- 
portional to the coefficient for rest ; but as the impact of each 
blow starts the key, the effort causing motion is determined by 
the value of the coefficient for rest, and this effort is, when P 
is the pressure on the key, 

F = P tan cp + P tan (a + cp) ; 

the work done is, when W is the striking weight and v its 
velocity, 

W^- = Fs = Ps [tan (a + <p) -f tan cp)] ; 

while for backing out the key, 

F = P tan [tan (<p — a) -f- tan cp] ; 

W ——Ps [tan {cp — ex) + tan cp] ; 
2 g 



THEORY OF FRICTION. 37 

s being the space through which the resistance /'maybe taken 
as acting. Maximum rigidity and inelasticity of parts would 
make s approximate o. 

When tan (cp — a) -\- tan 9=0, cp — a= — cp, and a = 2cp ; 
and with this value of a no force is needed to " slack" the 
key. For well-finished keys, f— o.io, when the surfaces are 
not lubricated more than is commonly the effect of handling, 
and a may be taken above io°, i.e., a taper of about one to six ; 
more usual values are I : 50 to 1 : 100 for keys fitted to gibs, and 
half these values for cotters, or keys without gibs. 

28. The Distribution of Pressure on surfaces subject to 
wear by the friction of motion depends greatly upon their form 
and on the character of that motion. Plane surfaces, if rigid 
and subject to the wear of straight-sliding parts, of which they 
form the bearing surfaces, if originally well fitted and of homo- 
geneous material, and if kept in good order, exhibit uniform 
intensity of pressure throughout, when the resultant pressure 
passes through the centre of figure, and sustain uniformly vary- 
ing pressure when the resultant is outside that centre. In the 
latter case, the mean pressure may generally be assumed as a 
uniformly distributed pressure in calculations. Inequality of 
pressure leads, first, to unequal wear, then to exaggerated 
variation of intensity of pressure, and finally to " cutting," or 
abrasion, and destruction of the wearing parts. The maximum 
permissible intensity of pressure is generally the less as the 
speed of rubbing is the greater, and is usually but a small 
fraction of that representing the " elastic limit " of the metal 
resisting it. 

Plane surfaces subject to wear under a motion of rotation, 
even where the pressure is at first uniformly distributed, are 
apt ultimately to take such form that the pressure is of vary- 
ing intensity. The method of variation will be dependent 
upon the form, and the fitting of the journal to its bearing. 
As an example, a disk rotating about its centre will usually 
wear differently at the periphery and toward the centre, and 
thus ultimately is caused such a distribution of pressures as 
will throw the greater part of the load upon the central part of 



33 



FRICTION AND LOST WORK. 



the disk. The tendency is usually to effect such a distribu- 
tion of pressures as will finally give permanence of form. 

Curved surfaces may thus take pressure in many ways ; but 
it probably rarely occurs in practice that the pressure is of per- 
fectly uniform intensity. A number of cases will be considered 
in the succeeding articles. The most important case is the fol- 
lowing : 

A cylindrical or spherical journal, if perfectly fitted, when 
unloaded will, with its bearing, take such a form under load 
that the intensity of pressure on the bearing surface will vary 
as the cosine of the angle made by a radius passing through 
the given point in that surface with that radius with which the 
resultant pressure coincides. Thus : 

In the figure, let ACB be 
the trace of the bearing surface 
of a perfectly fitted unloaded 
journal. When the load comes 
upon it, the journal will sink a 
minute distance, OO f , CC ', into 
the bearing, slightly compress- 
ing the metal, and taking the 
-e new position A'C'B'. As the 
maximum intensity of pressure 
in any well-proportioned jour- 
nal is usually but a small frac- 
tion of that which would pro- 
duce a compression exceeding 
the elastic limit of the metal, 
and as within that limit the resistance is directly proportional 
to the compression, every part of the surface, as E, will be sub- 
ject to pressure of intensity proportional to the displacement, 
EI, of that point in the bearing. Thus the pressure at B re- 
mains, as at first, zero, and contact simply is preserved ; at E 
the pressure is proportional to EI, and at C to CC. But the 
vertical displacement, CC, BB' , EJ, is at all points the same, 
and the compression, EI, at any point, E, being very small, is 
measured by the product of that constant quantity into the 
cosine of the angle, COE = 8, between the radius, OE, pass- 




Fig. 9. — Distribution of Pressure. 



THEORY OF FRICTION. 39 

ing through that point, and the line of the resultant bearing 
pressure, OC. 

The sum of all vertical components of these normal pres- 
sures, each of which latter is measured by the product of a 
constant into cos 6, is equal to the total load, W. Hence, 
taking the intensity of pressure at any point, £, as represented 
by p, and the constant as p n the pressure on any element, afr, is 
pds, — assuming the length of the element unity, — and this is 
equal to/ y cos dds. The vertical component, w, is 

w = / cos dds = p { cos 2 dds ; 

and the total load and the value of p t are 



W: 



A /cos' dds; Prj^z 



r' dr 

But cos 6 =s /— 5 r , and ds = ■ s = dr sec ; then 

Vr, — r cos 6 ' 



JT: 



= *<*</*' VrJ^P = Ar '' sin _1 ^ = ^ A r ' ; W 

a = t^; ; < 2 > 

and the pressure on unity of area, at any point, E, is propor- 
tional to cos 0, and is 

WcosO 

* = -^7 (3) 

when r, is the radius of the journal. 

It is evident that a similar demonstration applies to the 
case of the sphere. The amount of compression is determined 
by the magnitude of the modulus of elasticity of the softer 
metal of journal or bearing, and by the intensity of pressure. 
Thus, for a maximum pressure of 1000 pounds per square inch 



40 FRICTION AND LOST WORK. 

(703 kgs. per sq. cm.), a pressure often attained with steel crank- 
pins, and with a modulus of elasticity of the bronze bearing of 
12,000,000 (843,600 kgs. per sq. cm.), the maximum compres- 
sion would be but 12 ^ 00 th the thickness of the " brass," or, for 
journals of small size, about 0.00004 mcn (0.000 1 cm.). This 
distribution of pressure remains constant so long as the maxi- 
mum pressure is less than that producing wear. 

In all cases which are to be here considered, W\s the resul- 
tant pressure on the bearing surface. It is found by combin- 
ing the weight of the parts carried by the journal with the 
effort acting upon the journal, directly or indirectly, and pro- 
ducing or tending to produce motion. The distribution of 
pressure under light loads and at high speeds is sometimes 
determined by the action of the lubricant, as illustrated in ex- 
periments with the " oil-bath." This treatment is exact for 
cylindrical shell-bearings in rigid frames, approximate only for 
other cases. This investigation exhibits plainly the desirability 
of securing the greatest possible rigidity of frames carrying 
bearings. 

29. The Friction of " Journals," as a source of lost work, 
is of great importance to the engineer. A journal is a surface 
of revolution, turning, loaded with a pressure due the weight 
of the shaft and its load, within another surface of revolution, 
called the " bearing," which should be of the same form, and 
which should perfectly fit the journal without pinching. 
These surfaces are almost invariably cylindrical ; but they are 
sometimes conical, sometimes conoidal or ellipsoidal, and rarely 
of other related forms. Axle or shaft journals, gudgeons, and 
trunnions are the familiar forms of this element of mechanism. 

A journal in thoroughly good order will fit the bearing 
throughout the arc of intended contact : it is the custom with 
many experienced engineers, however, to " free" the bearing at 
the sides, leaving the two surfaces in contact only for about 
one half the total depth of the bearing-piece, i.e., over an arc of 
contact of 120 . Journals also frequently wear loose, and thus 
concentrate the load upon a limited area. Bearings are also 
sometimes bored out a very little larger than their journals, 
with a similar result. The theory of such cases is as follows : 



THEORY OF FRICTION. 



41 



(1) A loosely fitting journal, ABC, when at rest, will lie 
at the lowest point in its bearing ; but, when moving will roll 
up the side until it be- 
gins to slide ; it then 
retains this position so 
long as the coefficient 
of friction is unchanged, 
and rises and falls as the 
coefficient increases and 
diminishes, continually 
finding new positions of 
equilibrium. 

At any one instant 
there are three forces in 
equilibrium : the weight, 
W, on the journal; the reaction, N t of the bearing; and the 
force of friction, holding the journal at the line of bearing on 
the inclined surface : this latter force is F = fN. The angle, 
FDE = a, between the tangent to the common surface of con- 
tact and the horizontal is evidently that of an inclined plane 
on which the mass would slide with uniform velocity, and 
hence tan a =f= tan cp. These forces being in equilibrium, 
they may be represented by the " triangle of forces," DNB. 

Then, since the forces iV and .Fare at right angles, 




Fig. 10.— Loose Bearing. 



VfT = N l + F* ; 

= (i+/ 2 )^ a ; 



(0 



N = 



F = 



W 



Vi +/ 2 
fW 



Wtzn cp 



Vi+f' 2 Vi+tztfy 



= Ws'm <p\ 



(2) 



(3) 



and the motion of the journal carries it around, in the direction 
opposite to that motion, through the angle of kinetic friction, 
cp = tan -1 /", as above stated. 

The Moment of Friction is M = Fr n if r t represents the 



42 FRICTION AND LOST WORK. 

radius of the journal, and the energy expended or work done 
is U= aFr /f per unit of time, when a is the angular velocity. 
Hence this moment is 

M =Wr, sin <p = -ff^-, .... (4) 

and the energy wasted, or work of friction, per minute or per 
second, 

U= War, sin <p=-^p^; ... (5) 
= 2 Wnnr. sin q> == ■■ / ' - Wn ; . (6) 

Vi +/ 2 v ; 

when n is the number of revolutions made in the unit of time. 

(2) A perfectly-fitted bearing may be made by careful work- 
manship and fitting, while unloaded, when constructed ; or it 
may be obtained by the wearing of the journal down into its 
bearing. In the first case, the pressure on the bearing gradu- 
ally increases, as has been seen, from o at the diametral line to 
a maximum at the bottom, this pressure being at every point 
proportional to the elastic, radial, displacement of the surface 
where pressed. In the latter case the bearing wears until the 
sum of the vertical components of all such elementary pres- 
sures — which sum is equal to the load — is so adjusted as to 
check the wear, and this may give a distribution of pressures 
in any manner intermediate between the preceding case and 
one in which the pressure is uniform through the supporting 
" box," the latter value of the intensity of pressure being a limit 
which may be closely approached, or even actually attained. 

For the first of these cases, the pressure on any elementary 
portion of the arc of the bearing, dd, is 

N / = plr / dd; ....... (1) 

in which N' is the normal pressure on an elementary area, 
lr,dd, which has the length of this journal, /, and the breadth 



THEORY OF FRICTION. 43 

r^Oyp being the intensity of pressure at that part of the arc 
considered. The sum of all the vertical components of these 
normal pressures is equal to the load W. Then 



»0 = + 



W=f J* plr x cos 6d9. 



7T 



But the intensity of the pressure, /, will be zero at 6 = -> in- 
creasing as cosine 6 to a maximum. p x , at 6 = o; therefore, 
since/ = P t cos 0, 

IT 

W = pjrj cos 2 Odd; .... (2) 

e = -~ 

2 



= />»(? + isin;r); 



= I.57/A; (3) 

W 

A^tjfc 1 (4) 



. ^cos<9 
/ = °- 6 4 jp ■; (5) 



/ max = 0.64 7 -- (6) 



/r 



The intensity of the force of friction at any element is 

. WfcosS 
.# = 0.64-^ — ; (7) 

and, at = o, (fp) max. = 0.64—^- (8) 



44 FRICTION AND LOST WORK. 

The total pressure on the bearing is 



+; 



P , = o.64wf 2 cos Odd ; . . (9) 



= 0.64W2 sin -; 
2 



= 1.27^. 
The total force of friction is 

fPW= I.27/W; ...... (10) 

and the work wasted is 

U = /Fs = 1.27/Ws) (11) 

in which s is the distance traversed by the rubbing surface. 
Otherwise the moment of friction is 

M = Ffr, = 1.27 fWr x \ .... (12) 

and the energy lost is, per unit of time, 

17= Ma = i^yfWar, = 2.^fnr x W7t. . . (13) 

Hence, in a bearing thus fitted, if the unloaded journal 
is an. absolutely perfect fit, the total friction is 1.27 times as 
great as with a loosely fitted journal. 

(3) A bearing in which the journal is so grasped as to give 
uniform pressure throughout, produces a loss of power which 
is also easily calculated thus : 

The intensity of pressure is at all points constant, and may 
be represented by p x . The vertical component is p x cos 6 ; 



THEORY OF FRICTION. 45 

and the total weight, W, sustained by the journal is equal to 
the sum of all vertical components. The pressure on any 
element is pjr \d6 ; its vertical component is pjr x cos Odd, and 
the total load is 

W=pjrj cos Odd; . . . . (i) 

e 1= -- 



= 2pjr x ; (2) 

^ = w; ( 3 ) 

Then the total pressure on the surface of the journal or of 
the bearing is the product of this intensity of pressure into its 
area, or 

P'=PM.', - • (4) 

= %7tW= 1.57 JT. 

The total force of friction is 

Ff=i.$7fW. (5) 

The moment of friction is 

M = P'fr x = i.tf/Wr,; . . .'. (6) 

and the work of friction is, per unit of time, 

U=Ma = afP'r 1 = i.$7afWr 1 ; .... (7) 

=fnWr l7 t*; .... (8) 

i.e., it is 1.57 times as great as in the loosely-fitted journal, and 
20 per cent, greater than in the last case. 



46 FRICTION AND LOST WORK. 

The first of the three cases just considered is often met 
with, new journals being often purposely or carelessly bored to 
make a loose fit, and old journals often wearing loose. The 
second case arises when the journal is made an exact fit, when 
new and unloaded ; and the last occurs when it has been 
running smoothly and without jar, and has thus gradually 
worked down into the bearing and has worn all portions of its 
surface to a small but usually appreciable extent ; such a 
journal is always found to be in excellent condition. The 
usual case in practice lies between these. The last case may 
be also met with in those rare cases in which a new journal has 
been fitted tightly into its bearing, and yet oftener where, as 
sometimes happens, the heating of the " brass" causes it to 
grasp the journal, closing over it so tightly as to cause as great 
heating on the sides as on the bottom. The Author has some- 
times met with such action in his own experience, even with 
very large journals and bearings. 

It is seen from the theory just developed that, while in any 
journal the total pressure and the total resistance at the sur- 
face of the journal are the same for any given load, whatever 
the size of journal, the moment of friction increases with the 
diameter of the journal, and the work lost varies in the same 
ratio. It will be also noted that, since the liability of a journal 
to heat varies directly as the intensity of pressure and as the 
amount of work done, and inversely as the area across which 
this heat can be discharged, the diameter of a journal does 
not within certain limits affect this phenomenon. This will be 
better shown in another chapter. The bearing should evidently 
be so proportioned that serious lateral pressures shall not be 
produced when in operation. 

With a flooded journal, as where the oil-bath is used, the 
pressure is probably nearly always a maximum at the meridian 
line, becoming zero at the edges of the brass. The second 
case is therefore correct here. 

(4) The quantity of heat produced by the friction of the 
journal, in the several cases above treated, is obtained by divid- 
ing the work of friction by the mechanical equivalent of heat. 
Calling this J, and its reciprocal A, we have for the loose bear- 



THEORY OF FRICTION. 



47 



ing, Case I, H representing the heat produced in the minute or 
the second, whichever may be the unit of time. 



H= -y=AW=z 2AWnnr 1 sin <p; 



= 2 A Wnnr, 



f 



For the second case, that of the perfectly fitting bearing, 



(i) 



H — 1. 27 A Wafr 1 = 2.54A Wfnnr x ; 



(2) 



and for the last case, that of a tightly fitted bearing and uni- 
form pressure, 



ff=i.S7A Wafr x = A Wfnrfr,. 



(3) 



(5) The power demanded to drive the journal against its own 
friction, i.e., the power lost at the journal, is measured in horse- 
power by dividing the work thus done per minute or per sec- 
ond by the value of the horse-power, i.e., by 33,000, or 550 foot 
pounds, or by 4500, or 75 kilogrammetres. 

(6) A cylindrical journal turning in V's is a rare but not 
unknown case. Let ADB 

be such a bearing: let C 
be the shaft revolving in 
the direction of the arrow. 
It is evident that the shaft 
will tend to rise on the 
side A, and to relieve the 
side B from part of its 
weight. Hence the nor- 
mal pressures iVand N' 
will not be equal. The 
normal pressures N and 
N' t combined with the frictional forces F and F\ will give the 
component forces, Q and Q', respectively at the points A and B, 




Fig. ii.— Friction in V's. 



48 FRICTION AND LOST WORK. 

and these two forces must be in equilibrium with the force P 
acting through the shaft. Then, since NAQ, N f BQ = cp, 
QOP=NCP-q>- Q'OP=N'CP+<p. Calling NCP and 
h'CP equal to a, QOP = a — cp and Q'OP= a -f cp. 
From the triangle of forces formed by Q, 0, and P, 



Q==p sm(a-cp) t & _ p sm(a+<p) 
^ sin 2« ' sin 2a 



which expressions give the normal pressures N and N\ and 
thence the force of friction is found to be 



F = (N + N') tan cp, 



sin (a — cp) + sin (of + a?) J „cos a? sin a? 

= P ~ ! — — cos cp tan cp = P -. 

sin 2«r cos a 



Where the friction is slight the angle cp will be small, and 
cos cp may be taken equal to I ; then the value of the force of 
friction for a triangular bearing will become 



„ „ sin cp 

F=P £ 

cos a 



In an ordinary free journal, however, this friction is 
F= P sin cp. 



Hence the friction of a triangular journal is greater than 

in a free cylindrical journal. 

If ADB = 6o°, a == 6o° and = 2, or the friction of 

cos a 

such a journal would be twice that of a journal bearing on the 

bottom of the " brass." 






THEORY OF FRICTION. 49 

For a = 90 , or when the shaft bears on opposite sides, 
= 00 , and the friction is infinite. For the case of a close- 



cos a 

fitting journal, or one bearing at all points of the brass, 



F= Psin cp 



2.XQ.AD 



sin a 




Friction of Journal. 



If a = 90 , sin a = 1, and AD = 1-57; hence the friction 
isi^= i.57Psin /?, or 1.57 times 
greater than that of a free bear- 
ing, as before found. For a = 
30 , or when the axle bears only 
on |-th of its circumference, we 
have sin a == 0.500 and arc AD 
= 0.5236, and F— 1.0472/* sin 
<p, or only 1.047 times that of a 
free bearing. 

When a, is very small the 
arc AD = sin a, and the formula reduces to Psin cp, or the fric- 
tion for a free bearing. 

The Length of Journal may be determined when the con- 
ditions giving a measure of the resistance and work of friction 
are known, and is evidently nearly independent of the diame- 
ter ; since a variation of diameter but slightly affects f y and 
hence does not greatly affect the value of the quantity of work 
pVf, upon the value of which the work done on the unit of 
area, and therefore the working of the journal, mainly depends. 
The intensity of pressure, p, being reduced by enlarging the 
journal, the velocity V is correspondingly increased. A limit 
to length of journal is usually fixed by assuming a safe value 
for that product, as 60,000 for well-made crank-pins, 40,000 for 
locomotive-pins, or for journals well protected from dust and 
on which the pressure is unintermitted. This principle may 
be shown thus : The work of friction is fP m nnd = U\ the 
projected area subjected to pressure is equal to A = Id, and 



50 FRICTION AND 10 ST WORK. 

the work per unit of this area being taken, as a mean, at 
50,000/* foot-pounds, 600,000 inch-pounds, is 

U A _, nd . n 
Td = fP m n 1 j=fpmn J - 



i.e., 600,000/ = fP m 7t - ; 



P m 7tn „ 

/ = -z = 0.000005 Pn ; 

600,000 J 

_ 600,000 _ 50,000 
p= nnd ~~V~" 

If we give the diameter a fixed relation to length, i.e., /= ad, 



P = pld=ad*\ d 



= \-a 



while the diameter, calculated for strength against breaking, as 
in an end journal, is 

d<xJ~, 



where R is the modulus of rupture. Then 




v 






RV 
a 



5o,ooo£ a ' 
and 



a 



=cVRV= e 



\/y ; 



THEORY OF FRICTION. 5 1 

in which c ==: 0.0007 to 0.0009 for marine engine crank-pins, or 
c = 0.0004 for locomotives, and e = 0.05 to 0.06 and e = 0.08. 
Journals carrying unintermitted loads require longer pins. 

The pressure on journals is very generally reckoned, as 
above, by reference to the projected area. 

A Line of Shafting consists of a succession of iron or 
steel shafts, or axles, connected end to end by " couplings," 
and carrying often a set of pulleys or of gearing, by which the 
power transmitted to and through the line is distributed to the 
driving shafts of various machines. This is called " line-shaft- 
ing," to distinguish it from the " countershafts" and other 
shafting of special machines. 

Line-shafting is carried by a succession of bearings placed 
40 to 60 diameters of the shafting apart usually, and the 
journals are generally made three or four diameters in length. 
These journals sustain the weight of the shafting, pulleys, and 
belting, and the resultant pull of the belts, and are thus sub- 
ject to considerable friction and consequent waste of power. 
Since the power applied is all received at the end, it is evident 
that the size of the shafting may be economically reduced, as 
this power is distributed to the machinery driven in passing 
from the receiving to the farther end. 

Were this variation to be made by a gradual reduction of 
diameter, and were the power all transmitted to the farther 
end, the economical method of proportioning would involve 
the measurement of the friction, and the determination of such 
a size as would be the minimum required safely to transmit 
the effort demanded to overcome the friction beyond the given 
point, and to deliver the needed power. 

Resistance to torsion varies as the cube of the diameter of 
the shaft. Calling the diameter d, the moment safely applica- 
ble to the shaft is 

M=Ad\ (1) 

when A is a coefficient correct for the given case, and varying 
with the material and the magnitude of the factor of safety, 
which latter quantity ranges all the way from 6 to 30 in com- 
mon practice. 



52 FRICTION AND LOST WORK. 

If the weight of the material of which the shafting is com- 
posed be called w, the weight of a unit of length is 

w' — 0.7854W 2 ; (2) 

and its friction, nearly 

fw' = 0.7854/zm 3 (3) 

The moment of friction is 



fw' - = 0.3927/W 3 ; (4) 



and the "exhaustive length," as it is called by Rankine, which 
would be just sufficient to take up the whole applied moment, 
by its friction, is 

A 

Then the maximum resistance of the shafting is Ad 3 ; the 
moment of friction per unit of length is Bd z == 0.3927/w^ 3 ; 
and the moment demanded to turn a tapering line of shafting 
proportioned for minimum loss of power is 

Ad 3 = o.3g27fwLd z = M Q + 0.3927/22// d 3 dx, 

= Mo + Bj^d 3 dx, (6) 

when x is measured from the end farthest from that at which 
the effort is applied. Taking x = o at the nearer end, 

Ad 3 = B£° d 3 dx + Mo; ...... (7) 



THEORY OF FRICTION. 53 

M being the useful moment transmitted. Then calling d = y, 

$Ay*dy = By z dx ; 

A r d ^ dy r° , 
3Wa ^ = A dx > 



l_A 
B 



(ld&i<-log rf )=-/i .... (8) 



where */ x , */ , are the diameters of the shafting at the ends and 
/ the total length ; hence 

A ' d 1 7 

3 -s iog,^- = -4; 



4 = 4/ 3 ^ ; 



o 
BU 



= *S* (9) 

The diameter thus diminishes by a geometrical ratio, the 
variation of diameter of section of the shafting being repre- 
sented by a logarithmic curve. 

When the shaft is reduced, as is usual, by sections, each 
having a fraction, m, of the length of the whole line, the diame- 
ters diminish in a geometrical progression having the ratio 

( _^li\i 
V L) ' 

The work of friction on the line having a continuously re- 
duced section is 

U= BaJ o d 3 dx, 

Bx 



= Bad:f\ > A dx, 



Bl x 

lAad^e * A +3Aad ', . . . (10) 



in which a is the angular velocity of the shafting. 



54 FRICTION AND LOST WORK. 

30. The Friction of Pivots, often used to sustain the 
" end-thrust" of shafting, is of the same character as that ob- 
served in the usual forms of journal, but the forces are some- 
what differently distributed. A journal sustains a load applied 
in the plane of revolution of a shaft ; a pivot meets the resist- 
ance due to longitudinal pressures, and is usually a circular 
plane surface at the end of the shaft subjected to such " thrust.'' 
When the thrust is received by annular plane surfaces formed 
on "collars" moving with the shaft and resting on similar an- 
nular surfaces forming bearings, the theory is the same as for 
the plane pivot. Pivots are sometimes made conical and some- 
times of spherical surfaces ; they are occasionally given the 
form of a surface of revolution generated by the revolution of 
the tractrix. 

(1) The " Circular Plane Pivot " is not one of stable form. 
The velocity of rubbing increases from zero at the centre to a 
maximum at the periphery, and, assuming the intensity of 
pressure originally uniform over the whole surface, the ten- 
dency is to wear on the outer parts and to throw more and 
more pressure on the central portions, finally bringing the sur- 
face to a much more stable form, but to one which is probably 
rarely the same for any two cases. 

Assuming the intensity of pressure to be /, the total load 

W 

to be W. and the radius to be r, let — r = P' be the same 

throughout ; the normal pressure on any elementary ring, of 
the radius r and width dr, is 

N=2p f 7trdr\ (1) 

the elementary moment of friction is 

fNr = 2fp f 7zr*dr (2) 

The total moment of friction is 

M-=2fp'n £Vdr, 

= W*>i> 

= 1/^x5 (3) 



THEORY OF FRICTION. 55 

and the energy lost in the unit of time is 

U=Ma = \afWr, (4) 

symbols as before. 

Hence the resistance and the work of friction on the flat 
pivot may be considered as due the total load, resting on a 
pivot at a distance from the centre equal to two thirds the 
radius of the disk. This expression is equal to 

U=Ma = i7tfWr 1 n; (5) 

when n is the number of revolutions made in the unit of time. 
(2) The "Collar-Bearing" is a plane pivot, of which the 
central portion is removed ; its moment of friction is there- 
fore obtained by integrating the expression just given for the 
flat pivot between the limits of the two radii R x and R 2 of the 
collar. Thus 

M=2fp r 7t£>dr\ 

= t/^p^-p (0 

The work wasted by friction is 



V = Ma = \afW ^—7*- ■ ■ (2) 

'2 T \ 

These expressions reduce to those for the pivot when r x is 
made zero. 

In the case of the collar, the " mean lever," as it is called, 
which is fr 2 for the pivot, becomes equal to 

r, + Zi 1 fa z r $ = 6r *fa + ^) + fa ~ r ^ 

2 I2r, I2r, 



56 FRICTION AND LOST WORK. 

The expression for energy lost reduces also to 

U=WnW r f~^; ... . . (3) 

1 2 ' \ 

when the number of revolutions, n, made in the unit of time 
is introduced. 

(3) The " Conical Pivot " is made by shaping the end of the 
axle into a cone and fitting to it a bearing of similar form. In 
this case the normal pressure on the bearing surface instead of 
being equal to the total load, W, is increased in the proportion 
of radius to the sine of the angle of inclination of the cone, 
i.e., the half-angle of the cone. Calling this angle a, and re- 
solving the force, W> into components, JV, normal to the in- 
clined surfaces of the cone, we have 



2 sin a 



The friction-force is 



W 

F = 2fN = /-. — ; . . . . . . . . (3) 

J J sin a 1 KJJ 

its moment is 

W 

M = i/r-. — . ........ (4) 

iJ 'sin a v J 

Since the " mean lever" is two thirds r 19 and the work or 
energy wasted is 

[/ = Ma==iafr 1 ~¥rz; (5) 



W 



±7tr x fn~ — . (6) 



sin a 



THEORY OF FRICTION. 57 

By reducing the length of the coned part embraced by the 
bearing, the intensity of the pressure is increased, but the 
moment and the work of friction are reduced as the cone bear- 
ing is decreased in depth ; and it is thus possible, if the limits 
set by adhesion and abrasion are not passed, to make them 
less than with the plane pivot of usual proportions ; although 
reducing the diameter of the latter to the same extent will 
give still greater efficiency, as is seen by making a = 90 in 
the last expression above given. Conversely, a sharp-pointed 
pivot may have the friction and the lost work increased in- 
definitely by reduction of the angle a, and they become in- 
finite, for a = o. 

(4) A " Truncated Pivot " is a journal in the form of a trun- 
cated cone on the end of a shaft subject to thrust. Its friction, 
moment of friction, and work of friction are evidently the sum 
of those for the two parts into which it may be considered as 
naturally divisible ; and 



^ = f/^fe?; 



r 2 ' sin a ^ ' 

W(r 3 — r 3 ) 

U=Ma = Uf—?-- -; (2) 

6 J r 2 sin a v J 

=Wn E^nn (3) 

6 J r 2 sin a w/ 

The wear of this pivot will always in time throw the whole 
load on the flat face, provided that has area enough to carry it. 

(5) A Conical Pivot, loaded transversely, as in the lathe 
" centre," is subject to the same laws as the common pivot ; 
but since the load is at right angles to the axis, the expressions 
already given must be modified by substituting cos a: for sin<*. 
Then 

F = fWsQC<X) (1) 

M= %fr x W sec a; (2) 

U— Ma = \afr x Wszo, or; (3) 

= %xr x fnWsGca. (4) 



58 FRICTION AND LOST WORK. 

The heat produced by the friction of the flat pivot is 

= ±A Wfnnr, ; . (i) 

that of the collar-bearing is 

H=\A Waf- 



r: — r; 



rJ - r? ' 



r n 3 — r* 



= t AW/k*5—S;. .... (2) 



r, — r 



that of the conical pivot with end-bearing is 



H=%A Waf-^ 1 - ;....... (3) 

8 J sin a ' vo/ 



= 4-4 Wfnn-I^- ;...... (4) 

3 J sin « w 

and when this pivot is truncated, 

r 3 — r 3 
H=\A Waf \ . ' ; 
d y r 2 sin <x 

= ^hW£zj; ( 5) 

r i r i 

The same pivot loaded transversely gives 

H = f ^ JF*/^ sec « ; 

= |^4 Wfn7tr 1 sec <* (6) 

(6) A " Spherical Bearing," or a bearing composed of a 
portion of a spherical surface, is often used in mechanism, and 
especially for the " steps" of water-wheel shafts. 



THEORY OF FRICTION. 



59 



In such a case, if the bearing wears, as may often be the 
case, until the intensity of pressure, p n is uniform over its 
surface, or if it is so fitted origin- 
ally, the pressure on any element- 
ary ring of radius r, and so situated 
that its normal makes the angle 
6 with the axis of the shaft, is 
2pnrds. But the breadth of the 
ring, ds, is equal to dr sec 6 ; hence 
the pressure on an elementary ring 
is 2pnrdr sec 6 ; and the total pres- 
sure is obtained by integrating this 
expression after determining the 
values of p and of sec in terms 
of r. 

The value of/ will be usually variable, and, for a common 
case, may be taken as o at the horizontal diameter, and a maxi- 
mum at the lowest point in the " step," varying as the cosine 
of the angle 6. Then p—p' cos 0, and the total normal pres- 
sure is 




Fig. 13. — Spherical Step. 



N = 2p'n I sec 6 cos Ordr 



= P'xr*. 



2p'n I rdr ; 

... (1) 



The total moment of friction is 



M= 2fp'nrVdr\ 

= ifp'7tr;; (2) 

and the work lost from this cause is 

U=Ma = iafp' 7 rr 1 >; (3) 

= ^fP'nr: (4) 



60 FRICTION AND LOST WORK. 

To find/', in terms of the total load, W, we have the sum 
of all vertical components of the elementary pressures, 



W = 2p'n I cos 6 rdr ; 
= 2 P n Jo -^ rdr > 



whence 



= tP'xrf, nearly; (5) 



W 

' = ^V ■ • •. < 6 > 

M = /Wr i; (7) 

U= Ma = afWr x ; 

= 2fn7tr 1 W. (8) 

(7) For a journal (Fig. 13) of spherical surface, not a com- 
plete sphere, like the common "cup and ball" pivot, but less 
than a hemisphere in extent, taking r x as the radius of the 
sphere, r 2 as the maximum radius of the projection of the 
bearing on the plane normal to the axis, we have, as before, 
for the elementary normal pressure, assuming the intensity of 
pressure variable as before, 

n = 2j> f 7trdr; 
for the moment of friction, 

M= 2fp f 7tf r Vdr\ 

= \&*r; (1) 

For the work lost, 

U = Ma = \afp'nr* ; 

= iff*nr; (2) 



THEORY OF FRICTION. 6 1 

Then, to find/, 

cos Brdr ; 



/' 2 y r a r z 
— - rdr 
r 



= \P n ; • • . • (3 ) 






and, approximately, 



M = fW r ,_ {r \_ r:t .... (5) 



U=Ma= fW— 



= 2f7tWn— /-I — 3 . ... (6) 

(8) The heat developed by the friction of a spherical jour- 
nal, measured in thermal units, is, for the hemisphere, nearly, 

H=AWafr\ 

= 2AWfnnr; ........ (1) 

and for the smaller surface it becomes nearly 



H= A Waf 



r? - (r; - r;? 



= 2AWfn x r ,_ {r l_ r , )V ... (2) 

" Spherical " journals may usually be treated as bearing 
over the whole hemispherical surface in the manner described 



62 



FRICTION AND LOST WORK. 



in the examples just given. Where disks are used of which 
the surfaces are small portions of spheres of comparatively 
large radius, they may usually be safely treated as plane disks. 
They are often fitted to bear only near the centre, but wear 
soon gives them a larger area of bearing surface. 

(8) The " Tractory" or " Tractrix" Pivot is a pivot of which 
the generatrix is Huygens' curve, the " tractrix." This curve 
was proposed for pivots by C. Schiele, by whose name it is 
often known. The curve may be described by affixing a pen- 
cil-point to a heavy weight, placing the pencil on the point of 
intersection of the proposed curve with the maximum pro- 
posed diameter of the pivot, attaching a string to the pencil, 
with a length equal to the maximum radius, and then drawing 
the free end of the string along the axis ; the pencil-point will 
describe the tractrix. The tangent of this curve is evidently 
of constant length. The valuable property of the curve is that 
the wear due to friction is the same at all of the elementary 
rings into which the bearing surface may 
be conceived to be divided. 

Let 6 represent the angle, at any ele- 
mentary ring of the journal, between the 
tangent to the surface at that ring and 
the axis. Let r be the radius of that ring, 
and r x that of the pivot at the larger end 
of its bearing, and let / be the constant 
length on the tangent intercepted be- 
tween the two rectangular axes bounding 
the curve. Then the area of any ring is 
Fig. 14.— Tractrix. 27trds == 27trdr cosec 6. 
The normal pressure on that ring is (Fig. 14) 




j) ycIt 
N = 2p x nrdr cosec = 2±-J—— ; 

sin 8 



its vertical component is 

w = NsinO ; 
= 2p x nrdr\ 



THEORY OF FRICTION. 6$ 

and the total load is 



W 



= 2 Pi 7t f o rirdr =PSr?', 



and the intensity of the pressure is 



* W "• 



and equal to that on a flat pivot, assuming in both cases that 
wear has uniformly distributed it. 

The resistance due to friction on any elementary ring is 

fN — 2fpjcrdr cosec 6 ; 

the moment is then 

fNr — 2fp x nr l dr cosec d; 

dr I 

= 2fA7tr *s^d = 2 fP^r dr; 

=. 2lfp x nrdr. 
The total moment of friction is 

M = 2lfpjt£\dr = L fp x 7t . r, 2 ; 

which, when r x = /, and the pivot is thus given maximum 
supporting area, becomes 

M = r*fp x n = fWr x . 

The energy wasted is 

U = Ma = afp x r x ?t = 27t l r x fp x n = 2fnr x Wn\ 
when n is the number of revolutions per second. 



64 FRICTION AND LOST WORK. 

The heat produced is 

H= 2Afn*r?p 1 n = 2nAfr x Wn. 

The moment of friction with this pivot is thus equal to 
the product of the load, the coefficient of friction and the maxi- 
mum radius, and is one half greater than that of the flat pivot. 
Its advantage is considered to be found in the distribution of 
pressure and its regular wear. Its moment of friction is in- 
dependent of the length of the pivot. This pivot is some- 
times called the " anti-friction" pivot. 

31. The Friction of Cords, and of Belts or Bands, is 
usually intended to be a friction of rest. Where transmitting 
power, this is almost invariably the case ; where the band or 
cord forms a part of or acts the part of a brake, the friction 
is that of motion. The principles are precisely the same for 
both cases, the coefficient of friction merely having a different 
value. The cord is almost invariably wrapped about a cylin- 
der. 

When a flexible cord or band is wound around a cylinder, 
an effort being applied at one end and a resistance at the 
other, the total effort producing equilibrium or motion must 
equal the sum of the resistance and of the friction of the cord 
on the surface which it traverses ; while, if the applied force 
simply prevents motion, it is equal to the difference between 
the other two forces, friction always acting to prevent move- 
ment. The magnitude of the total resistance offered by the 
force of friction is determined by the intensity and method of 
variation of the normal pressure between the band and the 
cylinder, and by the value of the coefficient of friction. 

(1) The intensity of the normal pressure at any point be- 
tween the band and the cylinder is proportional to the tension 
of the band at that point. This is easily shown in several 
ways. Thus : 

Assume the cylinder to have a length unity, the band to 
enwrap one half its circumference, and to be frictionless. 
Then, the total of all normal elementary pressures throughout 
the band resolved, each into components parallel to the two 



THEORY OF FRICTION. 



65 



ends, P X Q X (Fig. 15), of the band, is equal to the sum of the two 
tensions at Q x and P x ; and 



Q 



1 -{-P l — 2P 1 = 2p x r x j o cos Odd = 2p x r x sin 6 ; 



when p x is the intensity of normal pressure and 6 is the angle, 
> FOB, between the radius to the 

point of contact and the radius 

normal to the tangent coincident 

with the " leading part," CP V of 
: the cord. Hence, if T is the ten-.^. 
. „ n 



sion and 6 = — , 
2 ' 



T=P 1 =p 1 r 1 sin-^^r,; 
p^p^r^T+r^ . . 



(1) 




and /, which is proportional to the Fig. 15.— Pressure of Belt. 
tension of the band. 

It is now evident that on a band subject to friction the 
pressure at every point in the circumference is proportional to 




Fig. 16.— Pressure of Belts. 



the tension of the band at that point ; since, considering any 
one point, this is true, and the varying friction on either side 



66 FRICTION AND LOST WORK. 

does not affect its equilibrium. It follows also that on belts 
subject to friction the pressure on the pulley under the band is 
variable, increasing from the side at which motion is resisted 
to the side at which the effort to produce motion takes effect, 
precisely in the proportion in which the tension on the band 
increases. 

The same proposition may be proven thus: Draw inter- 
secting tangents, BP lt AQ^ at any points near each other on the 
circumference, and call the angles, BOC, AOC t each 6. Then 
the resultant of the two forces, Q lt P v will be 

*i = V(Q* + ^ 2 + 2QA) cos (i8o° - 20) ; 

and if the points are very near together, we may take Q 1 = P x 
and 

R; = 2/>"(i -cos 20); 

= 2P?.2 sin 2 6 (2) 

Making the intercepted arc indefinitely small, we have, at 
the limit, sin 6 = dd, and the arc is dd, calling P x = T, the ten- 
sion 

R? = 2P*. 2d6* ; 
R 1 = 2Tdd; 

*-£r**+'> (3) 

(2) The Resistance of a Band or Cord to slipping on a cy- 
linder, or of a belt on a pulley, is a logarithmic function of the 
two tensions. It is thus determined : 

At any given point the difference of the tensions on the two 
sides of that point is the measure of the force of friction at 
that element of the cylinder, and, as shown in the preceding 



THEORY OF FRICTION. 6? 

proposition, this is proportional to the tension there existing. 
Then we have 

dT = fp,r,dd = /Tdd; (i) 

r TldT ' s r a 
J Ti -f-fJ Q dd\ 

loge5=/0; jt = A (2) 

and 

F=T 1 -T 2 = P 1 -Q 1 =T 1 (i-e-S>); . . . (3) 



7! 



(/'-:);. ...... (4) 



If t = t = N, 



F _ N 



T = P = = F 



!_,-/» N-\ 



F F 

T* = Q x = e /e-i = tf _ j ; (5) 

The mean tension on the belt and its ratio to F are 
T x +T % TJLi+eS*) 7; +7; T t (i+e*) 

2 - 2 2^ ~27;(^-I)• 

Calling = 2zr«, in which n is the number of turns or the 
part of a turn which the band or cord makes around the cylin- 
der, and reducing for common logarithms, calling the modulus 
M, 

T = e-f* = \o*f* Mn = io 2 -? 288 /* ; 



since 



ef Q = gfmn — jQO.434294/0 — j 2.7288/» . 



6S FRICTION AND LOST WORK. 

and 

T 

common log -^ = 2.7288/0 ; 

T x - 7;= ^(l-IO-^SA); 

= r 2 (l- IO*7»«*/« _ 1) ; . (6) 

j? — 2.729 /« ^r 

1 = I — IO ' " = I0 2 '729/« _ I • • W 

For the quantity 2.7288/;* may also be substituted 0.00758 
/<9 when 6 is expressed in degrees, and 0.434294/$, if in cir- 
cular measure, common logarithms being used in both cases. 

The moment of friction is 

M^Fr^r^-T,); (i) 

and the work done in the unit of time is, as a maximum, 

U=M a = af- 1 (T 1 -T^; 

= 27rnr 1 (T l -T 1 ); .... (2) 
or per revolution, 

U=2nr l (T 1 -T,) (3) 

The values of M and of U may be less than the above, but 
cannot be greater. 

(3) In a " strap-brake" the band or strap is sometimes in- 
tended to slip, the tensions being just sufficient to control the 
load. In this case the value of / is that of the coefficient of 
friction for motion. Here motion occurs between strap and 
pulley, and heat is produced to the amount of 

H=2Axr 1 {T i -TJ (4) 



THEORY OF FRICTION. 69 

The work and the moment on a slipping-strap are always 
maxima ; if not slipping, the moment may be anything less, as 
where the brake sustains at rest a small load. 

The total friction-force is seen, both for the belt and the 
brake, to be independent of the size of the cylinder upon which 
it is coiled, and to depend solely upon the angular extent of 
the circumference embraced or upon the numbers of turns 
taken by the band, the ratio of tensions becoming rapidly 
greater as the strap is wound on ; thus, if /= 0.333, as taken 
by Weisbach, we have 





EXTE 


NT OF 


WINDING. 




T x 


e 


n n 






ef» 


T> 


90° = 


2 = 


\ revolutions 


JQO-2254 


1.788 


180° = 


71 = 


\ 


ti 


IO°-4548 


2.85 


360° = 


27t = 


1 


a 


I o°-9°96 


8. 121 


720° = 


47! = 


2 


a 


JQI.8IQ2 


65.95 


1440° = 


87T = 


4 


a 


j o3- 6 384 


4349 


2880° = 


i6tv = 


8 


a 


j Q7-3768 


18,914,800 


3650° = 


I07t — 


10 


a 


lQ9-og6 


1,247,380,000 



The total amount of work lost by friction in any case is, as 
has been seen (7^ — 7!,) S, when the space, S, traversed by the 
effort, T v is given. 

(3) The Friction of a Cord or Belt passing over the edge 
of a rigid body is determined by the amount of the change of 
direction taking place at the angle supporting it, by the value 
of the coefficient of friction, and by the magnitude of the two 
forces acting on either side the edge. If the edge is sharp, the 
cord may be stretched with such force as to cut it, and the 
resistance then becomes greatly increased ; but if the edge is 
smoothly rounded, and the cord perfectly flexible and unin- 
jured, the case is that of the friction of a cord on a cylinder of 
very small radius, on which an arc is enwrapped by the cord 
equal to the angle included between the two parts of the cord 
or belt. The resistance due to friction has been seen to be in- 
dependent of the radius of curvature of the arc, and it is evi- 
dent that the case is precisely that already considered. 



?0 FRICTION AND LOST WORK. 

Hence the friction is 

F — fR=T x — T*— T 2 (io*-™s* — i) ; 
= W(io 2 -7 2 9f» — I) ; 

— ^( IO o.oo 7 58/fl — l); . . . (i) 

when Wis the load and n and 6° are the measures of the angle 
in parts of a circumference and in degrees, respectively. 
The value of the pulling force is then 

— I0 -°°758/d^ .... (2) 

An approximate expression for the resistance of friction for 
small angles is obtained by taking it as 

F= «f+ 1) P+W) sin?; 

= ( 2 +f) HP'sinj, nearly (3) 

Where several edges are met, as in the " rendering" of a 
chain over a barrel of polygonal section, the faces of the poly- 
gon being equal in length to the links, the total friction may 
be calculated by introducing the sum of the angles, d, into the 
first of the above forms, (1), or by raising the last (3) to a 

T 

power, n, equal to the number of angles, the ratio of-^ 1 thus 

■* a 

increasing in a geometrical ratio : 

J P=^[(2+/)sinf]r (4) 

The work wasted is 

FS= WS (jo*>™s* - j) (5) 

The useful work is WS and the total work PS, 



THEORY OF FRICTION. 



n 



The following table gives the ratios of P : W 'for arcs less 
than 300 . For larger arcs see the preceding table. 



Values of — - for Belts and Cords. 

■Li 



Angle 0. 


Values of f. 


Degrees, 


Circular 


Parts of 










0°. 


Measure, 0. 


Circumf., n. 




0.3 
Values of 


0.4 
Tx -i- 7V 


0.5 










30 


O.52 


O.08 


1. n 


1. 17 


1.23 


i-3 


45 


O.79 


O.13 


I.17 


1.27 


1-37 


1.48 


60 


I.05 


O.17 


1.23 


1-37 


1.52 


1.69 


75 


1. 31 


0.2I 


1.30 


1.48 


1.69 


1.92 


90 


1.57 


O.25 


1.40 


1.60 


1.87 


2.19 


I20 


2.09 


0.33 


1-52 


1.88 


2.31 


2.85 


ISO 


2.62 


O.42 


1.69 


2.19 


2.85 


3-7° 


180 


3-i4 


O.50 


1.88 


2.57 


3.5i 


4.81 


2IO 


3-67 


O.58 


2.08 


3.00 


4-33 


6.25 


240 


4.19 


O.67 


2.31 


3.51 


5-34 


8.12 


270 


4.71 


075 


2-57 


4. 11 


6-59 


10.55 


300 


5.24 


O.83 


2.85 


4.81 


8.12 


13.70 



32. The Friction of the Wedge, and of the Screw, 

which is essentially a wedge, and both of which are illustrations 
of the inclined plane, has already been given in principle. 

(1) Applying these principles to the case of the wedge 
(Fig. 17), we have the weight, or 
force driving the wedge, equilibrated 
by the two lateral pressures and the 
frictional resistance to slipping on 
the sides ; and, a being the angle of 
the wedge, 

^=2/>sin^ + 2 /Pcos-; 



= zP (sin I +/ cos I )..(!) 

When the wedge is forced back 
by the lateral pressures, 

W=2Pf sin ~—f 




Fig. 17. — Wedge. 



cos 



f) 



(») 



72 



FRICTION AND LOST WORK. 



For other cases, simple and obvious modifications of the 
theory of the inclined plane already given will suffice. 

(2) For the screw, which is to be considered an inclined 
plane wrapped around a cylinder, the pitch of the screw meas- 
ures the height, the circumference is the length of base, and 
the length of thread of screw per revolution is the length of 
the inclined plane. We may take a (Fig. 18) for the angle 
at the point of the wedge or inclined plane, r the radius,/ the 
pitch of the screw or the height of the inclined plane, P the 
force applied at the end of the lever-arm r, PTthe load, and N 
the reaction at R normal to the plane. Then, resolving parallel 
and perpendicular to the plane, we have 





f 




r 


V 


1 ■< 








> 
V 


t 
V 









Fig. 18.— Screw. 



Pcos a ±fN— Wsma = o; 
P sin a — N -f- Wzos> a = o ; 

and hence, for limiting values, 



P sin a q=/"cos a 
W ~~ cos a ±_f sin a 



■ (1) 



The limits of value of the effort 
required at the end of a lever, or 
wrench, of the length r r , is evi- 
dently 



r^pL^w^ ™"^/™" . ... (2 ) 

r r cos a ±_ f sin a w 



The values of P and P may be any values between the limit- 
ing values thus derived. 

The case of the weight being raised by an active effort, P, is 
seen to be similar to that in which W acts to produce motion 
and P resists ; the expression for the one being identical with 
that for the other, with the sign of f changed. The value of 
Pis thus a maximum when an active and a minimum when a 
resisting force. 

Friction-Couplings consist of a solid and a hollow cone, each 



THEORY OF FRICTION. 73 

on the end of a shaft, and so fitted that they may be forced 
into contact, the one within the other, in such manner as to 
make a firm connection when desired. The lever-arm is, as 
has been seen (§ 30), 



r 



— 3. 



r; 



and the intensity of pressure is 



W 



A{s'\n ^a -\- f cos ^a)' 

when W is the total effort, A the area of common surface of 
contact, and a the angle of the cone. Then the resistance due 
to friction is 

F=fpA - * - 



sin \ct -[-/"cos \oc f 

W A W 

p max. = -j2 t " max. = pA = —?- ; 

and the limit becomes* 

F max. = fAp max. = W. 
For the plane disk, F max. = fW, 

33. The Friction of Gearing is partly due to sliding of 
the teeth upon each other, and partly to resistance to rolling. 

That part of the work lost by sliding is measured thus : 
Let a and /? be the angles made by the directions of motion of 
the two teeth engaged with the normal to their surfaces at the 
line of contact, and let P be the intensity of the normal pres- 
sure. Then the resistance to sliding will be 

R=/P. (1) 

* See Weisbach, vol. iii. 



74 FRICTION AND LOST WORK. 

The work done against this friction will be, if s is their rela- 
tive motion, 

U= Rs = fPs = fj\v x tan a + v, tan fi)t, . . (2) 

when v l and z> a measure the absolute velocities of the two teeth* 
Where several teeth are engaged, 

U = 2Rs = 2fPs. , . . . . . - (3) 

The loss of work and energy by friction of the teeth of 
gearing may be also measured thus : 

Let the angular velocities of two teeth in contact be a', a! ', 
and call the distance of the line of contact from the pitch-point 
of either tooth, s' . Then the relative velocity of rubbing is 
v' = (a! -\- a")s\ and the work expended in friction is 

U = fPv't = fPs'{a' + a")t (4) 

The loss due to rolling resistances is usually so small that it 
may be neglected ; but the method of calculation is given in 
Art. 25. 

In Screw Gearing, in which a screw or "worm" revolving 
in the plane of the gear drives the latter by engaging tooth 
after tooth as they come around, the loss of work is mainly due 
to sliding friction, and is often considerable. Here the resist- 
ance is, at the surface of the tooth, 

R=fP- (5) 

The work lost is 

U=Rs=fPs; 



= fnPV47t 2 r* + f; ... (6) 

in which r is the radius of the worm and / the pitch, while n 
is the number of revolutions made in the given time. 

When 8 is the inclination of the worm-thread with the axis 
of the worm, the total resistance is 

r ~ ■ tan 6 -f ' ■ ■ {7> 



THEORY OF FRICTION. 75 

in v/hich P' is the effort at the pitch-line tending to turn the 
i worm, and R is the resistance at the same point, but on the 
surface of the wheel, and in the plane of its rotation. 
When we make/= tan <p, 

F = R! cot (0 - <p) (8) 

The waste of power in worm-wheels is usually large — 
seldom less than one half, and often much more, as will be 
seen in a later chapter. 

34. The Rigidity of Cordage and of Chains is due to 
the internal friction and distortion in the first, and to the fric- 
tion of the links in the second case. 

Coulomb, studying the resistance of pulleys and of cordage, 
was the first to appreciate the importance of that element 
which arises from the stiffness of the rope. He found experi- 
mentally that it consists of two parts, one of which is constant, 
while the other is variable with the load. Calling the constant 
part A, and the variable part bP, we have, as the total resist- 
ance due to stiffness, A -\- bP, of which A results from the 
natural stiffness of the cord, and the rest, bP, is due to the in- 
crease of stiffness consequent upon the added load, P. 

Coulomb also found this resistance to vary inversely as the 
radius, or the diameter, D, of the pulley, and the total thus to 

vary as — ~ — . He also found that the character of the 

material and the " lay" of the rope influenced this quantity 
seriously. 

Thus the resistance increases with the increase of tension 
on the rope, and is measured by a constant number plus the 
tension multiplied by a constant coefficient. The resistance is 
also inversely as the radius of the pulley, sheave, or other 
cylinder on which the rope is wound, and as a function of the 
size of rope which appears to be variable with its character, 
material, and condition. This resistance is supposed to be 
due partly to the rigidity and molecular friction of the strands, 
but very largely, if not almost entirely, to the friction produced 
by the slipping of strand upon strand as the rope is bent and 
unbent in passing on and off the pulley. 



7& FRICTION AND LOST WORK. 

35. The Laws governing the Rigidity of Cordage were 
determined by Coulomb, and the following approximate ex- 
pressions for these laws were obtained by him : 

R = d* -=z for new white rope ; 

J3 A + bP f 
R x == d* jz — for worn white rope ; 

A -I- bP 
R 2 = d jz — for packthread ; 

A + bP e 
R 3 = n jz — for tarred ropes ; 

in which expressions d is the diameter of the cord as below, n 
is the number of strands of tarred rope, and A and b are the 
quantities already given. R is the total added longitudinal 
resistance due to stiffness. 

The work, W, in foot-pounds, performed in simply bending 
the rope, is measured by the product of the resistance just de- 
termined by the length (L) of that part of the rope which is 
"rendered " about the sheave or pulley; i.e., 

/-// 2 
W = —jz- {A -f- bP) for new white rope ; 

Ld\ 
W x = —jz- {A -f- bP) for worn white rope ; 

W a = -p (A+ bP) for packthread ; 

Ln 
W % = -=j {A -f bP) for tarred rope. 

Weisbach proposes an expression for this resistance of 
simpler form than the above : 



THEORY OF FRICTION. 



77 



in which K and a are coefficients to be determined by experi- 
ment ; P is the pull on the rope, and r the radius of the pulley. 
His experiments were made with larger ropes than those of 
Coulomb. 

Reuleaux uses a still simpler expression for belts running 
over smooth-faced pulleys: 



R = 



aAP 



in which R is the added resistance due to stiffness, as before ; 
A the cross-section of the belt, P the pull, and r the radius of 
the pulley ; a is an experimentally determined coefficient, 
which may be taken as 0.3 for leather, in British measure, or 
0.012 in metric measures. 

Eytelwein uses a similarly simple expression, 



R = 



ad 2 P 



for the resistance due to rigidity of cordage, which expression 
may be used for ordinary work. For r in feet and d in " lines," 
a — 18.6, and the resistance, R, is expressed in pounds for 
common rope. 

The constant coefficients given by Coulomb's experiment 
are as below. The unit of weight is the pound, that of length 
is the foot. 

WHITE ROPE. 





Diameter in 


Value of 


Value of 


Diameter in 


Value of 


Value of 






Inches. 


A. 


b. 


Inches. 


A. 


b. 








lbs. 






lbs. 






* 


0.4 


O.40 


O.O08 


0.4 


O.40 


0.008 


) 3 




£0.8 


1. 61 


O.032 


0.8 


1. 14 


O.053 O 


5! 


Q i-6 


6.44 


O.I28 


1.6 


3-22 


O.064 vj 







3-2 


25.75 


O.511 


3-2 


9.IO 


O.180 


1 R 


0.4 


O.80 


O.O08 


0.4 


O.80 


O.OO8 


c 


<u 


-' 0.8 


3-22 


O.032 


0.8 


2.28 


O.053 J 


^ 




£ 1.6 


12.88 


O.I28 


1.6 


6.43 


0.064 S 





3-2 


5I.5I 


O.511 


3-2 


18.20 


O.180 


J p 



78 



FRICTION AND LOST WORK. 



TARRED ROPE. 



No. of Threads. 


Weight per Foot, 
lbs. 


Value of A. 


Value of b. 


6 
15 
30 


0.02 
O.05 
I. OI 


O.I5 
O.77 
2-53 


O.O08 
0.020 
O.040 



Weisbach's coefficients are : 

British. 



For tarred rope, 
For untarred rope, 

For wire rope, 

For tarred wire rope and 
hempen core, 



a — 0.22; 

K = 0.19; 
a = 0.0645 ; 

.AT= 1.08; 
a — 0.094; 

K= 1.21; 

# = 0.027 ; 



Metric. 
— l -l 

a — 0.006. 



K= 1.5; 



^T = 0.086 ; 
^ = 0.00164. 

K = 0.49 ; 
^ = 0.0024. 

•^=0.57; 
^ == 0.0007. 



The resistance of belts to flexure may be calculated by 
means of the simple formulas just given, and is expressed in 
terms of the tensions thus : 

The resistance due to flexure is, according to Reuleaux, 



R = 



aAP 



But the pull, P t is 



T — T 



and 



R 



= (?1±^(1 + L) ( (I) 



when the whole circuit of the belt about both pulleys is taken, 
and when r v r v are their radii. 



THEORY OF FRICTION. 79 

The work lost is then 



l L +;); 



U = Rs = %{T X + T}aAs\-- 

a may be taken as already given. 

36. The Friction of a Pulley or " Tackle" is due to two 
distinct phenomena : the friction of the pulley or " sheave" 
on its axis, i.e., the pin fixed in the " block," and the rigidity 
of the rope wound over the sheave. The first of these two 
resistances is that of the cylindrical journal. 

The load being W, the added resistances due these two 
causes, reduced to a common line of resistance with W, being 
F -\- S, the total load becomes, for a single block, 

F = W+F+S (1) 

The work done usefully will be Wh> where h is the distance 
traversed by the load, and the total work will be 

Fh = (W+ F + S)k (2) 

The methods of calculating the magnitude of these several 
forms of resistance have been already given. 

37. The Friction of a System of Pulleys is the sum of the 
frictions of all the elements of the system ; but as the load 
transmitted from pulley to pulley or sheave to sheave between 
the weight and the " hauling part" is continually augmented 
by added frictional resistances, the relation of the one quantity 
to the other must be determined by ascertaining the relations 
of these quantities for each. 

If the ratio 

F_W±F+S_ 

w~ w ~ u K) 

for a single pulley be known, and if this ratio be determined 

~F 
for each pulley of the whole system, then the ratio, =, for the 

W 



8 ° FRICTION AND LOST WORK. 

system is obtained by the continued multiplication of these 
values of C, and is 

~C=C 1 .C a .C,.€„etc ( 2) 

The final value of = is then known, P being the value 

which exceeds the value of P~, in a similar but frictionless 
system, in the proportion in which TTexceeds unity. The rela- 
tion of the effort, P, required to raise any given weight, W, in 
any frictionless system of pulleys may be experimentally de- 
termined from the relation of velocities of the hauling and the 
lifting parts. Thus, if these velocities are Fand W, 

Z YL 

w~Y (3) 

since, friction aside, the power or energy exerted and absorbed 
is the same at both ends of the system and 



PV=WV. (4) 

Then, friction being considered, 

CP ~p 

W = W ; CP=R (5) 

The relations between the effort exerted and the resistance 
overcome in systems of tackles are given in all treatises on 
mechanics. 

38. "Rolling Friction," or more correctly, resistance to 
rolling, is a consequence of the irregularities of form and the 
roughness of the surfaces of bodies rolling, the one over the 
other. Its laws are not as yet definitely established, in conse- 
quence of the uncertainty which exists in experiment as to how 
much of this resistance is due to roughness of surface, how 



THEORY OF FRICTION. 8 1 

much to original and permanent irregularity of form, and how 
much to distortion under the load. The first of these quanti- 
ties evidently varies inversely as radius : the second similarly, 
and the third as a function of the hardness and elasticity of 
the material of which the two bodies are composed. The 
total resistance, if the distortion does not exceed the elastic 
limit, is proportional to the load carried at the line or band of 
contact. In all actual cases the line of contact of two surfaces 
originally tangent and unloaded becomes a band, of which the 
width increases with the magnitude of the load and with the 
softness of the material. 

"Friction-Wheels" are often used to reduce the loss of 
energy at a journal, when the load is small, its direction con- 
stant, and the angular velocity small. In such case the jour- 
nal or " gudgeon" is supported on the periphery of two 
" friction-wheels," which are themselves supported on journals 
turning with an angular velocity less than that of the supported 
shaft, as the diameter of the journal is less than that of the 
friction-wheels. A single wheel is sometimes used, in which 
case the work lost by friction is reduced in the proportion 

^--' (I) 



when U v r x are the work done and the radius of the journal as 
ordinarily mounted, and £7 2 is the work done against friction 
when the friction-wheel is introduced ; r 2 is the radius of the 
friction-wheel. 

When two supporting wheels are used, 



£. ^L- ( 2 ) 

r n cos - 



in which a is the angle at the main journal-centre, subtended 
by the two friction-wheel centres. 



82 FRICTION AND LOST WORK. 

39. The Laws of the Friction of Rolling are as simply 
expressed as are those of sliding friction. It is customary to 
take this resistance as proportional directly to the load and in- 
versely as the radius of the rolling cylinder or wheel. Experi- 
ment shows, however, that, with wheels capable of yielding 
somewhat under load, the square root of radius should be 
taken in the formula for rolling resistance. 

The magnitude of the force of the friction of rolling is, 
therefore, at the axis, in the first case, 



W 



in which/" is the coefficient for the friction of rolling; W is 
the load on the line of contact ; and r is the radius of the roll- 
ing cylinder or wheel. Here the effort is taken at the axis of 
the rolling body; acting at the circumference of the roller or 
wheel, as where straight-lined surfaces have relative motion on 
interposed rollers, the force of friction becomes 



W 

i/Z (2) 



The first of these two cases is illustrated in ordinary vehicles, 
the second where a heavy mass on rollers has the hauling rope 
or chain attached to the mass itself. In the latter case, two 
frictional resistances are met — at top and at bottom of the 
roller. The moment of resistance is 

M=Fr=/W. 

The moment of friction is evidently thus measurable by 
the product of the load into an arm the value of which may 
be determined by experiment, and the resistance is thus plainly 
of the nature of a couple resisting rotation. This moment, 
multiplied by the relative angular velocity of the two surfaces, 
gives the work of rotation. The value of the arm as given by 



THEORY OF FRICTION. 83 

Coulomb and Tredgold are from/* =0.002 foot with iron to 
/= 0.006 for hard wood; the load being multiplied by this 
arm the moment of resistance is obtained. 

The work of rolling is evidently measured by 

Ma= [7=Fs=Wfs,. . . . . . (3) 

in which s is the space through which the carriage is drawn. 
The total work is this amount increased by the work of axle- 
friction, and that of raising the body against gravity in passing 
over the road. 

Friction Gearing is sometimes used. It is made without 
teeth, the periphery of the wheel being sometimes plain, some- 
times grooved, on the one shaft, and made of wedge-shaped 
section on the other, the one wheel driving the other by fric- 
tion. In such cases the adhesion is usually found greater than 
is due to ordinary friction-coefficients. 

In this case the work done against rolling resistance is 
measured by 

U=atP; (4) 

where a is the relative angular velocity, b a constant depend- 
ing on the conditions which affect rolling friction, and which 
will be given later ; and P is the total pressure with which the 
two wheels are held together. It is evident that the pressure, 
P, must exceed the driving effort, P\ in the proportion 

P 1 
JP=J> (5) 

or the surfaces will slip and the pair will refuse to drive. 

With grooved wheels the pressure applied to hold them to- 
gether may be reduced as the grooves are made with smaller 
angles. The value of /is, in this case, taken as that of the co- 
efficient for rest ; /= 0.15 as a minimum ; ^ =; 7. 



84 FRICTION AND LOST WORK. 

40. The Draught of Vehicles, a case which illustrates the 
first of the two methods of application of the impelling force, 
for rolling friction is a matter demanding careful investigation. 
Morin and later investigators disagree in their statements of 
its laws. The former, who made very extended experiments, 
states these laws as follows : 

(1) On hard surfaces, as paved and macadamized roads, the 
resistance is directly proportional to the weight of vehicle and 
load, inversely proportional to the diameter of wheel, and in- 
dependent of the breadth of wheel-tire. It increases with 
velocity. 

(2) On soft ground the resistance increases inversely as the 
breadth of tire. It does not sensibly vary with velocity. Morin 
concludes, also, that the line of draught should be horizontal. 

Dupuit, working with carriages on macadamized roads, 
found the resistance- to vary nearly inversely as the square 
root of the diameter of wheel, and directly as the load on the 
wheel. He found the resistance on pavement to be increased 
at high speeds by the concussions incident to rapid movement. 
Clark obtains a somewhat less simple law, which he expresses 
thus: 

R = a + bv+Vcv (1) 

The work of hauling is then 

U=Rs=(a + tv+Vcv)vt (2) 

This formula is deduced from the experiments of Macneil 
on " metalled " roads.* The values of the constants for the 
several formulas expressing these variously stated laws are, in 
British measures, a =30; & = 4; c = 10 pounds per ton, v 
being given in miles per hour ; these figures are derived from 
Macneil's experiments.f 

The resistance of all vehicles on common roads and streets 



* Clark's Manual, p. 964. 
f Parnell on Roads, p. 464. 









THEORY OF FRICTION. 85 

is principally resistance to rolling, their axle-friction being 
usually comparatively small. The work of hauling is, then, 

U=Fs=fWs=fWvt. ..... (3) 

Railway trains are subject to the same laws as are carriages 
on hard roads, although some elements of resistance here 
enter which are absent in the latter case. Their wheels are 
fastened rigidly to the axles, which rotate with them and 
compel both wheels on the same axle to revolve with precisely 
the same angular velocity. In turning curves, or where, as is 
not infrequently the case, the wheels differ in size, this arrange- 
ment gives rise to an increased resistance, which is sometimes 
very considerable. This increase of resistance cannot occur 
when the wheels are loose on the axle, as on other vehicles. 
Another source of increased resistance is the friction of the 
flanges of the wheels rubbing laterally against the rails. 

A principal resistance of trains at ordinary speeds is, how- 
ever, as with other vehicles, that of rolling friction. The re- 
sistance of railway trains is commonly reckoned, in British 
measure, in pounds of resistance per ton of weight of train. 
Clark makes this resistance vary as a constant plus a term 
which varies as the square of the velocity, thus : 

R = a + bv' 1 ; (4) 

the values of the constants in which are given by Clark as 
a = 6 to a = 8 ; b = -pL- to b = ^-J-g-, the first set applying to 
whole trains, the second to train exclusive of engine. 
The work of hauling is then 

Rs=(a+ bv*)s = avt + bv z t. 

On the best roads the resistance is often one half that given 
above. 

41. The Friction of Earth causes the retention of the 
form of elevations, or the preservation of embankments when 
soil is thrown up above the general level. The slope de- 



S6 FRICTION AND LOST WORK. 

pends usually upon the internal friction of the mass ; and the 
steepness of a bank of earth cannot permanently exceed the 
minimum angle of repose of the material of which it is com- 
posed under the most unfavorable conditions, as when soaked 
by rains or floods.* 

The resistance to displacement by sliding along any given 
plane, in such a mass, is equal to the normal pressure exerted 
between the parts of the mass on either side of that plane, 
multiplied by the coefficient of friction, i.e., the tangent of the 
angle of repose — of the material. Thus, 

F=p n tan <p t (i) 

where F is the resistance per unit of area, and p n is the inten- 
sity of pressure normal to the assumed plane. 

In order that no part of a detached mass shall slide, it is 
thus necessary that the angle with the horizontal made by the 
plane along which least resistance to motion is offered shall be 
less than cp. 

It is shown by Rankine, in the theory of the " Ellipse of 
Stress," f that the relation of maximum and minimum pres- 
sures must be such that 



and 



sin<f »K+% ■ •" • ? - ' * (2) 

A i + sin^ 

/, x — sin 9 ' ' ' ' " " " 



and hence that the ratio of their difference to their sum at any 
given point must not be greater than the sine of the angle of 
repose. 

It is also shown J that the intensity of pressure in a direc- 
tion parallel to the surface must be 

_ cos 6 — 4/(cos 2 6 — cos 2 cp) ' . 

p = WX COS 6 3— 2 — 5 r . . . (4) 

rv cos 6 -+- |/(cos 6 — cos cp) yrT/ 

* Rankine "On the Stability of Loose Earth," Phil. Trans., 1856-7. 
f Applied Mechanics, § 112. % Ibid., §§ i95~7- 



THEORY OF FRICTION. 87 

when w is the heaviness of the soil, x the depth of the point 
of application, and 6 the angle of surface slope. 

The intensity of vertical pressure at the same point upon a 
plane parallel to the surface is obviously 

p x — wx cos d (5) 

When the surface has assumed a permanent slope at the angle 
of repose, = cp and 

p y = wx cos cp=p x (6) 

When the surface is horizontal, 6 = o and 

p x = wx; (7) 

I — sin cp 
p y =wx — : — .— - (8) 

rv 1 -|- sin cp w 

Where the earth lies against a vertical plane, as the back of 
a retaining wall, the pressure in the direction parallel to the 
surface of the soil causes an effort which is equal to 

Py=£ H pJx, ( 9 ) 

cos — |/(cos 2 6 — cos 2 cp) 



= iwH 2 cos 6 



cos 6 -\- ^/(cos 3 6 — cos 2 q>) ' 



and the point of its application is situated at a distance below 
the top of the wall 

*e = f#: (10) 

When the surface of the soil lies at the natural angle of repose, 
9>= 6, 

P y = iwH 2 cos cp\ . ......... (11) 



88 FRICTION AND LOST WORK. 

When the soil is level with the top of the wall, = o, 

pgfrirL^*2 (I2) 

This force is applied at the depth x c = \H, and has a mo- 
ment 

P y x c = \wW * ~ Sm " 03) 

The moment of the wall about the outer edge is to be divided 
by a suitable factor for safety to determine a value which is 
to be placed equal to the above : 

— w'HV = M- = P y x c = \wH* LlLiyL£ . . ( I4 ) 
2a a y c 3 i + sin <p 

a rr3 i — sin <p ' 

M—-wH % — r — — — ; .'...■■.. (15) 
3 1 -f- sin cp y ^ DJ 



. \ — sin cp 2 aw . 

b = H\ — : — t—^-a/ ;; . . . (16) 

y 1 + sin cp Y 3 w' ' 



which equations apply when the overturning moment is a mini- 
mum. 

Where jar or shake produces a displacement by settlement 
of the earth behind a retaining wall, the maximum possible 
pressure may be encountered, and we shall have 

M _ aP y (max.)x c 
id 

2 1 -j- sin cp , . 
= -awH 3 — ! — : — r ; (17) 

3 I — sin q> x ' ; 



_ _ I -f- sin cp 2 aw . 

~ 1 — sin <p\f 3 * w' 



18) 



THEORY OF FRICTION, 89 

It is usually the safer course to assume these latter condi- 
tions, and to give structures receiving such lateral pressures 
the greatly enlarged dimensions and stability thus indicated. 

42. The Pressures on Retaining Walls which sustain 
level embankments are due to the resultant of the pressure 
produced by a fluid mass of equal depth and density, and the 
resistance to motion produced in such a mass by the friction 
of its particles. The magnitude of the intensity of this re- 
sultant pressure may be obtained from the expressions given 
in the preceding article, or the following treatment may be 
adopted : 

Three cases may arise : 

(1) The mass may be perfectly fluid. 

(2) The mass may be semi-fluid or semi-solid, and friction 
may act to reduce the pressure tending to cause the mass to 
slide or to overturn. 

(3) The mass may be of the kind last described, and its 
internal friction may act to intensify the pressure upon the 
back of the wall. 

The wall, when yielding, may either slide or overturn. It 
usually gives way by " bulging" on the face, and finally crumbles 
down: it thus often overturns ; it rarely slides on the bed of its 
foundation. 

The First Case is illustrated by masonry dams and by re- 
taining-walls subject to the pressure of wet quicksand or of 
other soil capable of free flow. 

In this case q> = o, and tan cp = f = o, in the preceding 
equations ; and the pressure at any given point, situated at a 
distance y beneath the surface level is of equal intensity in 
all directions, and is 

p = wy, (1) 

in which w is the weight of the unit of volume of the mass. 
It is a maximum at the bottom, where/ max. = wH. 

The total pressure on the unit length of a vertical wall is 
the mean pressure, from top to bottom, multiplied by the 
height H\ i.e., 

ydy = \uoIP (2) 



90 FRICTION AND LOST WORK. 

This is the pressure tending to cause the wall to slide. If 
the friction of the wall on its bed is less, i.e., if 

F = fW<P, 

the wall will fail. If 

F = fW>P, (3) 

the condition of stability in this respect is complied with, and 
the wall will stand. For security, we should have 

F-afW. (4) 

The point of application of this sliding effort, P, is deter- 
mined by ascertaining the mean lever-arm of all the elemen- 
tary efforts tending to overthrow the wall. Thus, the moment 
of any elementary force, pdy, about the base, calling y the 
depth from that point to the bottom, and taking unity of 
length, is 

m—pydy\ (5) 

and the total moment is 



pydy\ 
= wf o H {H-y)ydy = \wH\. . . (6) 



This quantity being less, or greater, than the moment of 
resistance of the wall, i.e., 

iWt>iwH\ (7) 

/ being the thickness of the wall, the wall will stand or fall 
accordingly. 



THEORY OF FRICTION. 9 1 

Adopting for the factor of safety, a, any desired value, the 
equation becomes 



\Wt = \awH'; t = i-^; ... (8) 

which gives the required thickness of wall. 

The point of application of the resultant pressuVe on the 
wall, measured from the bottom, is evidently to be found by 
dividing M by P\ i.e., 

y=^=iH. ( 9 ) 

The " Centre of Pressure" is the point of application of the 
resultant force, P, and is that point at which, if a force equal 
and opposite to P be applied, it would produce an equilibrium 
of efforts and of moments. Its position is measured from the 
surface, as above, and the depth of the centre of pressure is 
equal to the quotient of the moment of inertia of the surface 
divided by its statical moment, which latter is equal to its area 
multiplied by the depth of its centre of gravity. 

The total pressure on the surface is thus equal to the 
weight of a column of the fluid having that surface as a base, 
and a height equal to the depth of the centre of gravity of this 
area below the surface of the fluid. 

The Second Case is met with when a mass of earth piled 
against a wall, or an embankment sustained by a retaining- 
wall, settles against the back of the wall without jar or other 
action tending to increase pressure. In this case the pressure 
is less than that produced by a fluid mass of equal density, 
and is the less as the friction and adhesion of the soil are 
greater. The friction and adhesion attaining a certain limit, 
the soil stands without support ; or, passing this limit, it may 
even require the exertion of a force to throw down a vertical 
face. 

To determine the pressure on the back of a vertical wall, 
under the assumed conditions, we may use the equations 
already given, or let the angle PBG = cp represent the angle 



9 2 



FRICTION AND LOST WORK. 



of repose, or the angle at which the soil will lie undisturbed 
by gravity. Assume" 1 a plane, BE, along which motion may 
take place should the wall yield ; let its angle with the hori- 
zontal be called 0, and let its angle with BP be /?. 

As the angle fi increases from zero to go° — <p, the ten- 
dency to slide increases from zero to a maximum ; but the 
weight of the mass sliding, CBE, decreases from a maximum 




Fig. 19. — Retaining Wall. 

to zero. The pressure on the back of the wall is thus zero for 
either /3 = 90 — <p, or fi = o, and is a maximum at an inter- 
mediate value of /?. 

Let Wbe the weight of the mass sliding, CBE, and P the 
reaction of the wall, or its equal quantity, the pressure on the 
wall. An equilibrium evidently exists between these two 
forces, the pressure, P' ', on the surface BE, and the force of 
friction. Resolving perpendicularly and parallel to that sur- 
face, since CBE = 90 — 6, 



Wcosd + Psm 6^P' =0; .... (1) 
PFsin O-Pcos 8-fP=o; .... (2) 
W r (sin 6 -/cos 6) - P(cos 6 +/sin 0) = o ; 



and P = W 



THEORY OF FRICTION. 93 

sin 6 — f cos 6 



cos 6 -\- f sin 



sin 6 — cos 6 tan cp 

cos Q -\- sin tan 9?' • • • • \o) 

TTT tan — tan cp 

— Jy • 

1 + tan 6 tan cp ' 

- w ! +/tan B W) 

But HP = iw/T cotan = iwH* 



and hence, P = \wH' 



sin # ' 

1 — /cot 8 
1 + /tan6>" 



1 rra 1 — cot ^ tan ^ 
= ^^i+tanatan^ ; ' • • • • • (5) 

Vvhich becomes zero when 6 = <p, and when = 90 , as already 
indicated, passing through an intermediate value at which P 
becomes a maximum ; thus, when 6 = ^(90° — cp), 

4^ff^ta n '|(90^-^)^>=•* ^ e;^f^g|. . (6) 

The moment of P about the lower edge of the wall is 

M = \P.H=\wW l ~ S ! n ^ . . (7) 
3 6 i -f- sin cp v// 

The moment of the wall resisting rotation is, if t be its 
thickness and w' the " heaviness" of the masonry, 

M' = iw'Hf. ....... (8) 

These moments should be equal for equilibrium, but a 
factor of safety of at least 4 should be adopted. Then we 
have M' = 4M, and if the factor of safety is a, 

fa w 1 — sin cp . . 

t = H \ / - . — r . — : — .— - ; (9) 

y 3 w 1 + sin cp' yyj 



94 FRICTION AND LOST WORK. 

or, if a = 4, 

„ /i «/ I — sin a> 

t=2H\/ -, : r- 21 . (io) 

y 3 w I -J- sin cp \ J 

Values of the functions of cp are given in Chapter VI. 

The Third Case is illustrated by retaining-walls on which 
the pressure is intensified by jar or change of volume due to 
alternate freezing and thawing, the action of friction tending 
to retain the maximum pressure, and by foundations. 

Foundations, whether of structures or of machinery, resting 
upon soil, depend for their permanence and stability upon the 
friction of the particles composing it. The pressure upon the 
bed of the foundation causes a tendency in the earth below to 
slide laterally, and thus to permit the foundation and superin- 
cumbent structure to descend. The liability to slide is zero 
where the material is rigid, and becomes greater as the friction 
and cohesion of the soil decrease ; until, in freely-flowing soils, 
like quicksand and mud, the sole supporting pressure is that 
due the hydrostatic head measured from the surface to the 
given level, and is proportional to the density of the material. 

The maximum horizontal pressure resisting this sliding is, 
since the direction of friction-resistance is here reversed, and 
we have -[-/sin cp in place of —/"sin cp, and the reverse, 



p max. = wh 



I -f- sin cp 



sin cp' 



and the greatest pressure vertically is 

i + sin^ /i+sin^A" 

p max. = p max. = wh\ : J ; 

r r I — sin <p \i — sin cpl 

which pressure is that which would barely sustain the load on 
the foundation or would resist the thrust of earth, as described 
at the beginning of this article. If the factor of safety is taken 
as a, the pressure on the lower surface of a foundation is 
readily obtained as below. 

The supporting power of a foundation, and the resistance 
of a retaining-wall subject to jar or to the action of frost, is 



THEORY OF FRICTION. 95 

evidently always limited by the maximum value of p v for the 
given case, which is 



A = w y\ 



I -f- sin cp 



sin cp' 



the corresponding vertical pressure thus cannot exceed 

1 4- sin cp (1 -j- sin cpV 

p = a — ! — =— ^ = w y\ • I ; 

r v i — sin cp y \i _ sin cpl 

and the total weight which can be sustained is 



1 + sm <P\ 
p'A = Awy\ — — r-^-J ; 
r *\\ — ■ sin cpl 



and the limit allowable for the ratio by which the weight of 
the structure exceeds the weight of the displaced soil is, at the 
point of maximum load, 



p' (1 + sin 

m = — =- ' 



in cpV 

r-^J (II) 



wy \\ — sin cp, 

The total horizontal resistance is, at the side of the founda- 
tion, the same as on a retaining-wall exposed to jar, 

^ . 1 -4~ sin cp , „ 

Py = \w f • , (I2) 

v 4 ^ I — sin cp' K J 

acting at y c = fy of (13) 

below the surface, when y c measures the total depth of founda- 
tion-wall below the top level. 

Taking a as a factor of safety, the pressure on the lower 
surface of a foundation of the area A, carrying a load W, may 
be such that 

, = p' max.= awh ( - — S l n - ) ; . . . (14) 
A r \i - sin 9»/ v J 






9 6 FRICTION AND LOST WORK. 

and the area and the total weight should be 
W 



awh 



jl ( 1 + sin ^ y. 

\i — sin cpl ' 



w=aAWh (i±j^X. (I5> 

\i — sin cpl ^ •>' 



the weight of building, if uniformly distributed, exceeding the 
weight of soil displaced by its underground masonry in the 
proportion 



f i + sin <p V 
u — sin (pi 



Thus, for / == tan cp — tan 1 5 = 0.27, this value is r = 2.9 ; 
for cp = 30°,f= 0.58, r = 9; and for cp = 45°,/= 1, r= 34, 
nearly, the value of r and the stability of the foundation in- 
creasing with great rapidity as f assumes large values. Where 
jar occurs, the factor of safety must be very large, since this 
causes a direct tendency to relieve pressure, to reduce friction, 
and to cause to bow. 

Values of f, and of the more important of the factors above, 
will be given in Chapter VI. as derived by experiment. 

43. The Friction of Fluids, having its origin in condi- 
tions essentially different from those met with in the motion 
of solids in contact, is subject to quite different laws. When 
a fluid moves in contact with a solid, or when it flows in a 
current through a mass of fluid, precisely the same conditions 
arise. In either case, the resistance experienced is due to the 
relative motion of layers of fluid moving in contact with each 
other. 

At surfaces of contact with a solid, the fluid lies against 
the solid without appreciable motion ; as the distance from 
the surface of layer after layer is increased, the relative velocity 
of the fluid and the solid becomes greater up to a maximum, 
which is reached at the farthest point in the mass of fluid from 
the two bounding surfaces. This process can be readily ob- 



THEORY OF FRICTION. 97 

served by watching the behavior of the fine threads of marine 
vegetation often covering the sides of a ship below the water- 
line, while the vessel starts slowly into motion in still water. 
Fluid friction is, therefore, the friction of adjacent bodies of 
fluid in relative motion, and is due to the formation of small 
whirls or of large eddies in the two bodies, the production of 
which absorbs energy from the flowing mass. The friction of 
the fluid finally extinguishes this energy of eddy-motion, con- 
verting it into heat, and raising the temperature of the mass 
by the introduction of the heat-equivalent of the mechanical 
energy thus destroyed. The resisting property which thus 
effects this conversion, and which is the cause of fluid-friction, 
is called viscosity. No true friction-, in the sense in which that 
term is commonly used, has been recognized in fluids. The 
best evidence that it does not exist is, perhaps, the fact that 
the Iriction of fluids is unaffected by variation of pressure. 

44. The Laws of Fluid Friction are tolerably well estab- 
lished. They are, for all fluids, whether liquid or gaseous : 

(1) Fluid Friction is independent of the pressure between 
the masses in contact. 

(2) The Resistance of Fluids is directly proportional to the 
area of the surface exhibiting it. 

(3) This resistance is proportional to the square of the 
relative velocity at moderate and high speeds, and to the 
velocity nearly at very low speeds. 

(4) It is independent of the nature of the surfaces of the 
solid against which the stream may flow ; but it is dependent 
to some extent upon the degree of roughness of those surfaces. 

(5) It is proportional to the density of the fluid, and is 
related in some way to its viscosity. 

The resistance to relative motion, in cases of fluid friction, 
against solids, in ordinary work, may be expressed by 

R=fAV\ . . (1) 

calling f the resistance on an area unity, A the area of the 
surface exposed, and Fthe velocity of gliding of the fluid over 



9^ FRICTION AND LOST WORK. 

it. The relation of the total resistance to the head producing 
flow, h = — , is given by 

R=/wA^; (2) 

in which /' = -^, 

J w 

and w is the " heaviness" of the fluid, i.e., its weight per unit 
of volume. 

The work of friction is 

U=Rs = RVt=fAV 3 t', 

=f'Awt—. ... (3) 

The quantities / and /' are sometimes distinguished by 
calling /the resistance per unit of area of surface, and /' the 
coefficient of fluid friction. As stated already, these values 
are not absolutely constant with varying velocities, but must be 
modified often to meet special cases. Thus, Eytelwein takes 

/ = a + y ;........ (4) 

/=V+"^ • ' • '■;■;■ ■ • • (5) 



Weisbach takes 



Values of /and of/ 7 will be found in Chapter VI. 

They range from /= 0.0026 to / = 0.005 an d from f = 
0.0025 to/ 7 = 0.0049. 

45. Viscosity and Density, while they do not affect to 
any observable extent the rate of flow of fluids retarded by fric- 
tion, and do not usually affect the values of the coefficient, do 
nevertheless determine the total expenditure of energy in the 
production of the flow of a given volume at a given velocity. 
The fact that the coefficients used for the limpid liquids, as 



THEORY OF FRICTION. 99 

water, the vapors, as steam, and the gases, as air, and at all 
pressures, are in practice sometimes taken without serious 
error as the same, indicates that this resistance is in such cases 
a kinetic form of resistance rather than one due to intramo- 
lecular action. 

Viscous fluids, as heavy oils, molasses, tar, and viscous 
solids, as ice or the resins, follow laws which have not been 
fully ascertained ; but their flow is evidently greatly influenced 
by their molecular constitution. 

46. Molecular or Internal Friction is well known to 
exist in solids which can be made to flow. It is a form of fric- 
tion frequently observed, but not as yet fully investigated, and 
is still but little understood. 

One of the best illustrations is that described by Professor 
William Thomson. A copper wire was stretched by an in- 
termittently increasing load, and the successive elongations 
noted. The load was then removed by a similar process, and 
the successive decrements of length were also observed. It 
was found that the latter were not precisely equal to the 
former, although the wire finally regained the original length ; 
but that there seemed to have come into play some force re- 
sisting motion both ways, as does friction. 

It is also found that molecular displacements, once taking 
place in the action of externally originating forces, sometimes 
give rise to a less resistance when the operation is repeated : 
just as if an originally present frictional resistance had been 
partly overcome by the smoothing of the molecular path, re- 
ducing resistance as frictional resistance to sliding or rolling is 
reduced by repeated sliding or rolling on the same track. An 
illustration of this phenomenon is seen in the fact that a 
magnet thoroughly demagnetized is remagnetized more easily 
with the original polarity than in the opposite direction. 

A modification of this action is evidently operative in 
viscous solids ; and it is probable that it is also seen in the be- 
havior of the viscous liquids while changing form and while 
flowing in currents. 

47. The Compound Friction of Lubricated Surfaces, 
as it may be termed, or friction due to the action of surfaces 



IOO FRICTION AND LOST WORK. 

of solids partly separated by a fluid, is observed in all cases in 
which the rubbing surfaces are lubricated. In such instances 
the solids are usually not completely separated by the liquid 
film interposed between them, but partly rub on each other, 
and are partly supported by the layer of lubricant which is 
retained in place by adhesion and by capillary action. The 
rubbing together of the two solids produces wear, the amount 
of which is indicated by the rate at which the lubricant be- 
comes discolored and charged with abraded metal. The work 
of friction, both of solid and of liquid, is transformed into heat, 
and is disposed of as the bearing heats, principally by radia- 
tion and conduction to adjacent parts, and partly by the flow 
of the lubricant. In all cases some abrasion is indicated by 
the change produced in the lubricant, and some heating is 
usually perceived in the bearing. 

With very heavy pressures and slow speeds, the journal and 
bearing are forced into close contact, as is shown by their worn 
and often abraded wearing surfaces ; while with very light 
pressures and high velocities the journal floats on the film of 
fluid which is continually interposed between it and the bear- 
ing. In this case the friction occurs between two fluid layers, 
one moving with each surface. There are thus evidently two 
limiting cases between which all examples of satisfactorily 
lubricated surfaces fall : the one limit is that of purely solid 
friction, which limit being passed, and sometimes before, 
abrasion ensues ; the other limit is that at which the resistance 
is entirely that due to the friction of the film of fluid which 
separates the surfaces of the solids completely. 

The laws governing the friction of lubricated surfaces are 
evidently neither those of solid friction nor those of fluid fric- 
tion, but will approximate to the one or the other as the limits 
just described are approached. As will be seen later, the value 
of the coefficient of friction varies with every change of 
velocity, of pressure, and of temperature, as well as with 
change of character of the surfaces in contact. 

The laws of complex friction are considered at great length 
in the last chapter. 

Where mixed friction is met with, it will usually be found 






THEORY OF FRICTION. 101 

that its laws approximate to those of solid friction as the 
journal is run dry, and to those of fluid friction as it is flooded 
with oil. Thus a journal or bearing surface fed with oil by 
an oil-cup, and where no oil-grooves are used to distribute the 
oil, will exhibit a total friction in some cases nearly propor- 
tional to the total pressure, the latter being varied ; while 
similar surfaces flooded with oil, as by the oil-bath, offer a 
resistance sometimes nearly independent of the pressure, and 
but little, if appreciably any, greater with heavy than with 
light loads. A perfectly lubricated bearing should follow the 
laws of fluid friction, and its friction should be independent of 
the intensity of pressure produced by the load, varying as the 
square of the speed of rubbing. Such perfect lubrication has 
never yet been attained. 

For perfect lubrication, assuming it practicable with com- 
plete separation of the surfaces, the laws of friction would be- 
come : 

(i) The coefficient is inversely as the intensity of the pres- 
sure, and the resistance is independent of the pressure. 

(2) The friction coefficient varies as the square of the speed. 

(3) The resistance varies directly as the area of journal and 
bearing. 

(4) The friction is reduced as temperature rises, and as the 
viscosity of the lubricant is thus decreased. 

These laws will probably hold, even with the greases, which 
all become fluid when introduced between the rubbing surfaces. 

It is found by experiment, as stated later, that the perfec- 
tion of this form of lubrication depends upon the amount of 
fluid-pressure produced between the surfaces by forcing in the 
lubricant between them. This separation occurs to an impor- 
tant extent at high speed and less at low velocities. Hence, 
the friction of lubricated parts is often found to decrease at 
low speed with increase of velocity, while increasing at high 
speeds as velocity increases. 

48. The Limits of Pressure for Lubricated Surfaces 
are determined by the nature of the materials composing them, 
and by their smoothne-ss and exactness of fit, as well as by 
the speed of rubbing, the character of the lubricant, and the 



102 FRICTION AND LOST WORK. 

methods of its application. A higher pressure is usually per- 
missible on hard than on soft material ; although when the 
soft materials, as for example common white alloys for bear- 
ings, are well sustained by a harder metal, the heaviest pres- 
sures allowed by the lubricant may be carried. 

The more viscous the lubricating substance, and the stronger 
the capillary action taking it into the space between the jour- 
nal and the bearing, the higher the pressure safely carried. 
With increase of speed the maximum pressure is lessened, and 
it is usual to take the intensity of pressure as inversely as the 
velocity of rubbing. Values of / thus determined will be 
given in Art. 127. 

49. The Magnitude of the Waste of Energy by fric- 
tion is measured in horse-power by the expressions (British 
measure), 

fPV 
(1) Flat surfaces, HP = * 



(2) Cylindrical surfaces, HP 



33,000' 

fPRd 
127,000 



when /, P, and V are the coefficient of friction, the load and 
the speed of rubbing in feet, and R and d are the revolutions 
per minute and diameter of journal in inches. 

The Methods of Reducing Waste of Energy by friction in 
mechanism are based upon very simple principles. It is evi- 
dent that to make the work and power so lost a minimum it 
is necessary to adopt the following precautions : 

(1) Make the coefficient of friction the least by proper 
choice of rubbing surfaces and by the best lubrication. To do 
this we should have at least one of the rubbing surfaces of 
a granular metal, and if possible both — that one which it is 
easier to replace being of the softer metal. The surfaces 
should not be subjected to a normal pressure beyond which 
the lubricating matter will be expelled. For slides, a much 
less pressure should be taken than for journals, as they have 
not as free a lubrication as well-arranged cylindrical journals ; 



THEORY OF FRICTION. 103 

but this limit is best determined by reference to the speed of 
rubbing and the nature of the lubricant. 

(2) Make the space through which the friction is to act a 
minimum by reducing the diameters of all journals to the least 
compatible with safety under the stresses they are expected to 
sustain. The work done is independent of the length of the 
journal, except as it may modify pressures, and thus the co- 
efficient of friction. 

(3) Properly fitting the bearing surfaces, removing that por- 
tion of the bearing near the jaws, and transferring the bearing 
surface to the bottom, one sixth of the circumference of the 
journal may be thus removed. A journal well fitted cold is 
not necessarily a good fit after it becomes heated by friction, 
owing partly to the want of homogeneousness of the metal of 
the journal and bearing ; a worn journal has less friction than 
when new. It is a question whether all journals should not be 
brought to a proper bearing and given a high polish before 
they are considered fit to perform their office. It is now usual 
carefully to grind all cylindrical journals, and to secure a very 
perfect fit in the bearing before setting the machinery at work. 

(4) Giving the journals such forms and such size as will 
allow them to convey away the heat generated, either by 
radiation from their surfaces or by conduction through the 
mass of metal, to circulating water, to lubricating matter, or to 
adjacent masses. 

(5) Securing an efficient system of supply of the lubricant. 



CHAPTER III. 

THE LUBRICANTS. 

50. The Lubricants are of three classes : Solids, Semi-solids, 
and Liquids. The first class are usually minerals, as graphite 
and steatite ; the second class is principally composed of the 
animal fats, but includes also some of the vegetable greases 
and special preparations from mineral oils. In the third class 
are included a very great variety of oils derived from all of the 
three great kingdoms of nature. 

The Natural Fats and Oils constitute a large and well- 
defined group of organic compositions, having some analogy 
chemically to the compound ethers. Hydrocarbons constitute 
the principal and characteristic portion of each of these com- 
pounds, and as a rule the higher their proportion and the less 
the oxygen the higher the temperatures of fusion. The pres- 
ence of albuminoids in animal and vegetable fats and oils causes 
a tendency to a decomposition, resulting in the production of 
" rancidity." When thoroughly purified by the removal of 
the mucilaginous and albuminous portion, rancidity does not 
occur. These fats and oils are composed of stearine, marga- 
rine, and oleine in varying proportions; the former are solid, 
the latter is liquid at common temperatures, and the propor- 
tion in which these constituents are found in any fatty sub- 
stance determines its temperature of solidification or of fusion. 

The mineral oils and greases are originally derived from 
vegetable matter, but are so completely altered as to consti- 
tute a distinct class. They contain no oxygen when first ob- 
tained from the earth, and absorb it from the atmosphere but 
slowly and in usually insignificant amount. 

51. The Valuable Qualities of Lubricants determine 
their power of reducing friction and their endurance, as 



THE LUBRICANTS. 105 

well as that of the surfaces on which they are used. The 
amount of frictional resistance to the motion of machinery is 
obviously determined by the character of the lubricating ma- 
terial. Nearly all recent experiments in this field have been 
made in investigations of the value of lubricants which include 
very much more than a single measure of the coefficient of 
friction. The later determinations of the friction of lubricated 
surfaces at the various pressures and speeds which are com- 
monly met with in modern machinery will therefore be given 
after discussing the nature of lubricating materials, and the 
standard or other methods of ascertaining their value. The 
tables to be given later will serve the mechanic, the engineer, 
or the designer of machinery as data by means of which to 
estimate the probable losses of power by friction under every 
usual set of conditions met with in practice. 

The value of a lubricant, as a lubricant, is nearly independ- 
ent of the market price. Some of those materials which would 
be most useful in reducing friction, could they be so applied, 
are, however, entirely unknown to consumers of lubricating 
substances, because of their monopoly for other purposes, for 
which they are in such demand as to entirely remove them 
from a market in which other unguents can be obtained at 
comparatively low price. The best known lubricant for gene- 
ral purposes — sperm-oil — is far less used than the less excel- 
lent but cheaper lard oil, which in turn is less generally used 
than the mineral and mixed oils with which the market is 
always largely supplied. 

The effect of friction — rolling as well as sliding — is to wear 
and abrade solids, and with fluids as well as with solids, to 
generate heat to an amount which is the exact equivalent of 
the work of friction, and which, could it be all collected and 
measured, would be found to be a precise measure of the power 
wasted and lost in consequence of the friction. The amount 
of heat thus produced is equal to one British " thermal unit" * 
for each 772 foot-pounds of work expended in overcoming fric- 
tion. This figure is that known as Joule's " mechanical equiva- 

* A British thermal unit is the quantity of heat required to raise the tem- 
perature of a pound of water one degree Fahrenheit. 



106 FRICTION AND LOST WORK. 

lent of heat." Where the work is measured by the metric 
system this corresponds to the development of one " calorie' * 
of heat for each 424 kilogramme-metres of work done in over- 
coming frictional resistance. 

This evolution of heat has a serious ill effect in several 
ways : it reduces the viscosity of lubricants, thus rendering 
them more liable to exude from between the rubbing surfaces 
at high pressures ; it is cumulative, and causes danger to be- 
come more and more imminent as it progresses beyond the 
limit within which conduction and radiation may dispose of it 
to surrounding objects as fast as generated ; it causes serious 
injury to the surfaces in contact, cracking, distorting, and abra- 
ding them, and thus increasing the friction while destroying 
journals and bearings ; it often even ignites the lubricant, over- 
heating, softening, and weakening the abrading metals and en- 
dangering all combustible material in its neighborhood. The 
journals of machinery are often actually welded into their 
bearings. The burning of mills and of steam-vessels, and the 
breakage of car-axles, and consequent destruction of trains 
loaded with passengers, sometimes result from the use of im- 
proper lubricants or of badly proportioned rubbing parts. 

Since lubrication has for its objects both the reduction of 
friction and the prevention of excessive development of heat, 
the engineer resorts to the expedient of interposing between 
the rubbing surfaces a substance having the lowest possible 
coefficient of friction and the greatest capacity for preventing 
or reducing the development of heat. It is evident, then, that 
in order that any substance may be efficient as a lubricating 
material it must possess the following characteristics : 

(1) Enough "body" or combined capillarity and viscosity 
to keep the surfaces between which it is interposed from com- 
ing in contact under maximum pressure. 

(2) The greatest fluidity consistent with the preceding re- 
quirements, i.e., the least fluid-friction allowable. 

(3) The lowest possible coefficient of friction under the 

* The metric "calorie" is the heat required to raise the temperature of a 
kilogramme of water one degree Centigrade. 



THE LUBRICANTS. 10/ 

conditions of actual use, i.e., the sum of the two components, 
solid and fluid friction, should be a minimum. 

(4) A maximum capacity for receiving, transmitting, stor- 
ing, and carrying away heat. 

(5) Freedom from tendency to decompose or to change in 
composition by gumming or otherwise, on exposure to the air 
or while in use. 

(6) Entire absence of acid or other properties liable to pro- 
duce injury of materials or metals with which they may be 
brought in contact. 

(7) A high temperature of vaporization and of decompo- 
sition, and a low temperature of solidification. 

(8) Special adaptation to the conditions, as to speed and 
pressure of rubbing surfaces, under which the unguent is to be 
used. 

(9) It must be free from grit and from all foreign matter. 

Oils must be used with some caution when applied to jour- 
nals upon which other lubricants have been employed. It 
sometimes happens that two oils are entirely incapable of 
working together, and this incompatibility may cause trouble 
when they are used together, or even successively. A minor 
good quality possessed by some lubricants in greater degree 
than others is that of being readily removed, and allowing the 
bearing surfaces to be easily cleansed when they have become 
soiled and gummed by alteration of the unguent, and by the 
gathering of dust and abraded metal upon them. 

Oils should not be liable to decomposition by heat or wear, 
or to separation when mixed, either in use or by long stand- 
ing, or by alteration of temperature. They should, if mixed, 
always have the same specified composition. Uniformity in 
this respect is as important as excellence of quality of the 
normal mixture, and the quality of the oil is usually of more 
importance than the quantity. The adhesiveness of the oil to 
the metal, and the ease of flow, with minimum fluid-friction, 
are the essential characteristics of a good combination of 
materials in bearings and lubricant. Cast-iron is somewhat 
spongy in texture, and is therefore an exceptionally good 
metal for bearing surfaces, when of ample area ; a dense, 



108 FRICTION AND LOST WORK. 

smooth-surfaced metal is more subject to friction than the 
same surface finely scratched or slightly roughened. Surfaces 
may be too smooth.* The best mineral oils are often better 
in the above-mentioned qualities than the organic oils; and 
sperm, neat's-foot, and lard, for ordinary work, follow in order. 
The heavy petroleums are usually best for heated surfaces, as 
in steam cylinders, and often for heavy work on cool journals ; 
although many engineers still prefer the better class of greases, 
or even sperm-oil. 

The value of a lubricant to the consumer, as is seen from 
what has been just stated, depends on its cost in the market, 
its efficiency in reducing friction, its durability under wear, its 
freedom from liability to "gum," its freedom from acid and 
from grit, and its permanence of composition and of physical 
condition when subjected to changes of temperature, and also, 
frequently, its capacity for carrying away heat from journals 
already heated. 

Thus sperm-oil is one of the very best of known lubricants ; 
but its high price precludes its use, except for special purposes. 
Other oils are cheap, but have little lubricating power ; still 
others are good reducers of friction, but do not wear well, or 
cannot be retained on the journals ; others, as linseed and the 
drying oils generally, although sometimes excellent, otherwise 
gum so seriously that they cannot be used for lubrication ; 
while a good deal of the tallow in the market, and some other 
lubricants, contain acids of decomposition, or acids which 
have been used in their clarification, which have not been so 
completely removed as to prevent injury by their action on 
the metals. Some lubricants cannot be used at low tempera- 
tures because they are liable to congeal, and others cannot be 
used in steam cylinders, or where high temperature is liable to 
be met with, because they decompose or vaporize under such 
circumstances. 

Every dealer in oils and every consumer of lubricants who 
desires to know with certainty whether he has in any case 
precisely that lubricant and that quality which is nominally 

* Woodbury. 



THE LUBRICANTS. 109 

given him, must resort to some method of identification of the 
material. Every user of such a material who desires to know 
whether it is well adapted to a specific purpose, or who wishes 
to find out what are its peculiar characteristics, must find some 
method of testing it, and of thus ascertaining whether, under 
the conditions arising in his practice, it will serve his purpose. 
He must know whether it will bear the pressure, and will run 
without heating his journal at the speed to which he must 
subject it. 

As will be seen hereafter (Chapter VIII.), the price of an 
oil is usually of little importance in comparison with its fric- 
tion-reducing power. A saving of a few dollars' worth of oil 
at the expense of many times its value in heated and injured 
bearings, or in power and fuel, is extravagance. 

In order that the oil should retain its good quality and 
value, it should be so stored as not to be liable to alteration 
by the action of the air and of sunlight. Lubricants which 
do not adhere to the rubbing surface, which are wastefully 
fluid, which contain acids or grit are expensive to use, even if 
they cost nothing in the market. 

The following table shows the usual order of ordinary 
prices of the principal oils: 



(0 


Sperm Oil. 
' Seal Oil \ 


(2)- 


Olive Oil > These may change places at times. 




! Lard Oil ) 


(5) 
(6) 
(7) 


Rape-seed Oil. 

Other Seed Oils \ C° tt0 "- Se ed. 

( Linseed. 
Castor Oil. 




( Cod. 


(8) 


Fish Oils i Menhaden. 


(9) 


( Porgy. 
Whale Oil. 


(10) 


Mineral Oils. 


(11) 


Rosin Oil. 



I IO FRICTION AND LOST WORK. 

The Best Lubrica?its are in general the following, for usual 
conditions met with in practice : 

Under low temperatures, as in rock-drills driven by com- 
pressed air — light mineral lubricating oils. 

Under very great pressures with slow speed — graphite, 
soapstone, and other solid lubricants. 

Under heavy pressure with slow speed — the above, and 
lard, tallow, and other greases. 

Heavy pressures and high speed — sperm-oil, castor-oil, 
heavy mineral oils. 

Light pressures and high speed — sperm, refined petro- 
leums, olive, rape, cotton-seed. 

Ordinary machinery — lard-oil, tallow-oil, heavy mineral oils, 
and the heavier vegetable oils. 

Steam cylinders — heavy mineral oils, lard, tallow. 

Watches and other delicate mechanism — clarified sperm, 
neat's-foot, porpoise, olive, and light mineral lubricating oils. 

For mixture with mineral oils, sperm is best ; lard is much 
used ; cotton-seed and olive are good. 

Many different conditions must, therefore, be studied, and 
the behavior of the lubricant determined with reference to 
each before it can be known, with any degree of certainty, what 
is its real value for any specified purpose, and it is equally 
evident that the conditions under which the behavior of an 
oil or other lubricating material is to be determined should 
always be those approximating with the greatest possible ex- 
actness to the conditions proposed in its actual use. An exact 
theory of the commercial value of lubricants will be developed 
in a later chapter. 

52. Lubricants, as already seen, are sometimes solid, but 
usually liquid; and of the liquid unguents there are many 
varieties in the market, which differ in their viscosity and 
cohesiveness as widely as they do in nearly every other quality, 
and range from the most limpid watch-oils to those " heavy 
bodied " and densest of all the oils — castor-oil and rosin-oil. 
We have semi-solid lubricants, of which tallow, soap, cocoa- 
nut oil, and wax are illustrations ; and still others are perfectly 
hard and solid, as graphite and soapstone. 



THE LUBRICANTS. Ill 

The engineer also uses what are known as " anti-friction 
metals," one of the oldest and best known of which is the so- 
called " Babbitt-metal." These are permanently fixed in the 
bearings in the form of linings, and their peculiar use is to 
present to the journal, instead of the hard, unyielding, and 
resistant surface of the metal itself, a material which more 
readily and perfectly adapts itself to the form of the journal 
which it supports. 

Lead has been introduced by Mr. Hopkins to act thus tem- 
porarily, gradually, as it wears, letting the journal down to a 
good bearing on the brass of the boxes. 

Some anti-friction metals are used without lubricants, and 
are therefore themselves as truly lubricants as are plumbago 
and similar solid materials which are usually finely ground and 
interposed between rubbing surfaces. 

In some cases no lubrication will suffice to keep a journal 
from heating, or even " cutting :" in such an event the 
" brasses" are sometimes made hollow, and a stream of water 
is made to circulate through them, thus effectually keeping 
them cool. 

In the " Palier-glissant" of Girard and the " Water-bearings" 
of Shaw, the journal is supported upon a cushion of water 
which is forced into a space in the journal beneath it by a 
pump, and at such a pressure that the journal is perfectly 
"water-borne," and revolves on the liquid cushion. Shaw has 
applied this plan successfully in supporting vertical shafts. 

The Oils are the most generally applied fluid lubricants ; 
the most common are the better known and cheaper kinds of 
animal, fish, vegetable, and mineral oils : of these, sperm stands 
admittedly at the head of the list ; lard, neat's-foot, whale, tallow, 
seal, and horse oils are all largely used either alone or mixed. 
The vegetable oils in use are olive, which is by far most gen- 
erally used in other countries ; cotton-seed oil in the United 
States, palm, rape-seed, oleine, colza, poppy, pea-nut, rosin, 
cocoa-nut, and castor oils* are all more or less employed in 



* Linseed-oil is a good reducer of friction, but dries and "gums" too 
rapidly to permit its use as a lubricant. 



112 FRICTION AND LOST WORK. 

lubrication. Of the fish-oils, porpoise, cod, and menhaden* 
oils, are most used. The mineral oils are of two classes: 
the shale-oils, obtained from certain shales ; and the well- 
petroleums, which come from extensive oil-lakes, situated 
usually far beneath the surface of the earth, and which are 
principally obtained from oil-wells in Pennsylvania and other 
of the United States. Glycerine is sometimes used as a 
lubricant for light pressures. 

Of these oils, sperm excels nearly all others in its power of 
reducing friction, and generally excels them in endurance. 
Rape-seed is in some districts now displacing olive-oil as a 
lubricant ; but the mineral oils, pure or mixed, are rapidly 
taking the leading place in all markets.f 

53. The Semi-fluid Lubricants, or Soft Greases, are 
usually of animal origin. The term grease is usually restricted 
to those soft fats which permeate the tissues filling the cavities 
of the animal system, especially about the loins and among 
the intestines, and which are solid or nearly so at all tempera- 
tures not greatly exceeding that of the living animal. They 
usually liquefy at about this temperature, some of them be- 
coming fluid at even lower temperatures than the normal. 
Ignited, they burn freely, with a clear light, but with a smoky 
flame. 

The greases are composed of stearine, margarine, and oleine, 
in variable proportions, and are the more fluid as the latter 
constituent is present in larger proportion. They are partially 
soluble in alcohol, and freely so in ether, in essential oils, and in 
other oily compositions. When fresh they are white or light 
yellow in color, and when old and altered chemically or by 
mixture, often become darkened. They are always liable to 
alteration, becoming rancid on exposure to air and sunlight. 
This occurs by the development of the fatty acids, and this 
change, which is readily detected by their odor and taste, 
renders them injurious to the machinery on which they are 

* The whale is not a fish, but an animal classed among the mammals. 

f Portions of this chapter and of other parts of this work are from " Friction 
and Lubrication," lectures by the author, published by the Railroad Gazette 
Publication Co., New York, 1879. 



THE LUBRICANTS. 113 

used, and especially where heated, as in the cylinders of 
steam-engines. 

Tallow, which may be taken as the best-known example of 
this class of lubricating materials, is the fat of domestic animals, 
removed from the membrane in which it is secreted usually by 
melting. Its quality and properties vary somewhat with the 
animal, and with its age and other characteristics. It is solid 
at common temperatures, white or nearly white, slightly 
odorous, and readily saponifiable. The best is obtained from 
mature animals, and usually, according to Chateau and other 
authorities, from males of the domestic animals. The greater 
part of the tallow of commerce is beef tallow and mutton 
tallow. 

The greases are sometimes used in the natural state, and 
often mixed with other classes of lubricant. 

Vaseline, and other similar preparations of mineral origin, 
are to be classed with the greases, as are a number of vege- 
table waxes and butters, as the so-called cocoa-nut oil. These 
are rarely used in the lubrication of mechanism, however, 
although the former class occasionally and the latter more 
frequently are introduced into mixtures. 

Vaseline and the other mineral greases are obtained by the 
distillation of petroleum at low temperature in vacuo. The 
vegetable greases are usually natural products. 

54. For Hard Greases, as for use on railways, mixtures 
of tallow and palm-oil with water rendered alkaline with soda 
are often used. Two parts paraffine, one of lard, and three 
of lime-water is a good grease for heavy, slow-moving jour- 
nals. 

A mixture of eight parts of bayberry-wax with one of 
graphite is very good also, and is said by a U. S. Ordnance 
Board to be the best-known preparation for rifle-bullets. 

Grease is usually employed in lubricating axle-journals in 
Great Britain, and is generally of palm-oil. The following are 
said to be good compositions* for that climate : 

*W. R. Browne, Railroad Gazette, August 9, 1875 



114 FRICTION AND LOST WORK. 



Railroad Axle Grease. 

For Summer. For Winter. 

Tallow 504 lbs. 420 lbs. 

Palm Oil 280 " 280 " 

Sperm Oil 22 " 35 " 

Caustic Soda 120 " 126 " 

Water 1,370 " 1,524 " 

On German railroads the following composition is used : 

Parts. 

Tallow . 24.60 

Palm Oil 9.80 

Rape-seed Oil 1 . 10 

Soda 5 . 20 

Water 59-30 

100 . 00 

The following is Austrian : 

Tallow. Olive Oil. Old Grease. 

For Winter , 100 20 13 

For Spring and Autumn too 10 10 

For Summer 100 1 10 

Tallow and " black-lead," or plumbago, " white-lead " and 
oil, and mixtures containing sulphur are often used as semi- 
fluid lubricants. 

There exists a decided tendency to displace the more fluid 
by the less fluid lubricants, to use tallow in place of the oils, 
and to adopt manufactured hard greases where the more free 
flowing materials have been formerly generally employed. The 
change leads almost always, if not invariably, to loss of power 
by increased friction — a loss which is seldom noted — while 
saving in cost of lubricant by reduction of quantity used. In 
many cases this is not economy, and a careful determination 
and balancing of gains and losses is advisable before a final 
choice is made. 

The greases have advantages over the oils other than mere 
reduction of cost of lubricating material. The cost of the 
time demanded for the supply of the lubricant is usually less 
with the greases ; the drip is less, and the injury by soiling 






THE LUBRICANTS. 115 

floors and goods is correspondingly reduced ; danger of fire is 
also less, and the journals will usually work more uniformly 
cool. The greater the consistency of the lubricant, other 
things being equal, the greater its endurance and economy. 
The number of these greases in use is very great, and their 
differences of value are sufficient to make their careful selection 
by test a matter of serious importance. The method of appli- 
cation is even a more important matter than the kind of 
lubricant, or the conditions affecting it. 

55. The Solid Lubricants are sometimes found to work 
well when no fluid will answer at all. Some of them sustain 
immense pressures without injury. Those in general use are 
certain metallic compositions, mixtures of metallic with non- 
metallic elements — graphite, sulphur, soapstone, asbestos, lamp- 
black, and white-lead (carbonate of lead). In some cases they 
are permanently and solidly fixed, and sometimes are applied 
at intervals between the rubbing surfaces, as are the oils. 

Plumbago, or Graphite, and Soapstone are lubricants. The 
former is a solid form of carbon, supposed to be the ultimate 
product of the destructive distillation of the vegetable matter 
of the forests of the carboniferous or, usually, earlier periods. 
It is often distinctly crystalline, has a specific gravity of 1.8, 
and is moderately hard. Very pure graphite, containing 99 
per cent, carbon, is found at Ticonderoga, N. Y. ; in Cumber- 
land, Great Britain ; and in the island of Ceylon. Crude and 
impure graphite occurs in many other localities Very fine 
graphite also comes from Siberia, supplying the demand for 
the best grades of pencils. It is principally used for crucibles 
and in pencils, but is an excellent lubricating material for heavy 
work, and is also often found very useful for light machinery ; 
it is used for silk-looms making delicate fabrics which would be 
destroyed by. oil. Its value as a lubricant is sometimes greatly 
impaired by impurities, and especially if they are earthy and 
gritty. Freedom from such impurities is essential to the suc- 
cessful use of plumbago, either alone or mixed with other un- 
guents. 

Graphite was mentioned by Rennie in 1829: he states that 
"in all cases where plumbago was used it lessened friction," 



Il6 FRICTION AND LOST WORK. 

General Morin, experimenting with it later, concluded that 
it could be used to advantage where heavy pressures were to 
be sustained. The author has found graphite, and graphite 
mixed with certain oils, well adapted for use under both light 
and heavy pressures. It is especially valuable to prevent abra- 
sion and " cutting," under very heavy loads and at low veloci- 
ties. Plumbago is used generally by interposition, although 
often forming, as just stated, an ingredient in the composition of 
mixed oils and of anti-friction and "anti-attrition" compounds 
of the first class. It should always be absolutely pure and free 
from grit, and should be ground to the condition of a flaky pow- 
der. 

Mr. T. Shaw found it superior to oil for the tables of heavy 
planers. 

Soapstone is a hydrated silicate of magnesia, known also 
as talc and as steatite. It is very widely distributed. It is soft r 
easily cut by the knife, and has an unctuous quality, to which 
it owes its name. For use as a lubricant, it must be free from 
gritty impurities, and can be then employed like graphite. It 
is extensively used in the manufacture of " packing" for the 
piston-rods and valve-stems of steam-machinery. 

Some engineers express a preference for soapstone powder 
as a lubricant for the axles of machines. For this purpose 
it is first reduced to a very fine powder, then washed to remove 
all gritty particles, then steeped for a short period in dilute 
muriatic acid, in which it is stirred until all particles of iron 
which it contains are dissolved. The powder is then washed 
in pure water again to remove all traces of acid, after which it 
is dried, and forms the purified steatite powder used for lubri- 
cation. It is not generally used alone, but is mixed with oils 
and fats, in the proportion of about 35 per cent, of the powder 
added to paraffine, rape, or other oil ; the powder maybe mixed 
with any of the soapy compounds employed in the lubrication 
of heavy machinery. These solid lubricants are both used in 
making up packing for steam-engines, etc. 

Plumbago and soapstone are both used, mixed with soap, on 
heavy work, and especially on surfaces of wood working against 
either iron or wood. 



THE LUBRICANTS. WJ 

Asbestos is a silicate of lime and magnesia, having some 
resemblance to soapstone in its physical properties, but dis- 
tinguished by its structure, occurring in, often, long silky 
fibres. It is spun into threads and ropes, and woven into 
cloth, and even felted, and made into paper. It is used for 
piston-rod packing and if well purified is excellent for this 
purpose. 

Sulphur, " White Lead" and some other solids are used 
generally mixed with oils ; but they are not important mem- 
bers of the class of substances here considered. 

Woods, as lignum-vitae, beech, hickory, oak, maple, elm, 
canewood, snakewood, are sometimes used as bearing surfaces, 
and are almost always kept cool and prevented from wearing 
seriously by flooding them with water. The best of these 
woods are, like lignum-vitae, hard and tough in structure ; they 
are usually obtained from the tropics. 

56. The " Animal Oils" are usually derived from the fats 
of the mammiferous animals, including the whales and their 
relatives ; but they are sometimes obtained from fish, as from 
the " menhaden" or " moss-bunker." The principal of these 
oils are sperm and whale oils, lard and neat's-foot oils. Tallow- 
oil is also used to some extent. They are generally obtained 
by melting them out from the animal tissues in which they 
are originally found, and by passing them through various 
purifying processes. All have characteristic and persistent 
odors, which are often, as in the case of the fish-oils, disagree- 
ably powerful, and which are even perceived in the soaps made 
from them. The liquid animal oils are principally derived 
from the sperm and the " right" whales. 

57. Sperm Oil, or spermaceti-oil, is the best known, and 
for general purposes the most excellent, of all the lubricants. 
It contains, according to Brande : carbon, 78 ; hydrogen, 11.8; 
oxygen, 10.2. It is found in a large cavity in the head of the 
sperm-whale, mingled with the solid fat, spermaceti, from 
which it is separated by crystallization and pressure, without 
heating. It is saponifiable with potash, but with difficulty, 
and is one of the most permanent and most valuable of all the 
oils. Its specific gravity ranges from 0.880 to 0.896, averaging 



Il8 FRICTION AND LOST WORK. 

about 0.885. Crude " head-oil " from the cask runs about 
0.88. It is the lightest of all the lubricants. Sperm-oil is of 
light-orange color in large masses, lighter in small quantities, 
transparent, has a slight fishy odor, and precipitates needle- 
like crystals of spermaceti at 47 F. (8.3 C.J. It is solidified 
by nitric acid. 

Used as a lubricant, it is liable to sudden fluctuations of its 
coefficient of friction in consequence of its changes of density 
and fluidity, as the spermaceti contained in it alters with vary- 
ing temperature. In lubricating quality, for light work, as for 
spindles, it is only excelled by the very finest of the refined 
mineral oils, and excels nearly all other oils under heavy 
pressures, although often closely approached by fine petro- 
leums. Exposed to the air it absorbs oxygen, becomes gradu- 
ally " gummed " or resinous, and loses quality seriously. At 
140 F. (6o° C.) it gains two or three per cent, in weight in 
twelve hours. It has a " flashing point" at about 500 F. 
(260 C). 

Whale Oil is obtained from the " blubber" of the whale by 
removing it from the animal in great strips, which are then 
heated to melt the oil out from the tissues enclosing it. All 
the whales, including not only the varieties classed with the 
sperm and the right whale, but also the blackfish and their 
relatives, the dolphins, furnish this " train-oil." Three varieties 
of oil — the so-called white, yellow, and black — are brought into 
the market, and are mixed to form the oil of commerce. Com- 
mon whale-oil is brownish yellow, transparent, disagreeably 
odorous, limpid at ordinary temperatures, solidifying at the 
freezing-point, and precipitating at times more or less sperma- 
ceti. Its density is about 0.93 at yo° F. (21 C). It is much 
used in making crude soaps and for illuminating purposes, 
usually mixed with vegetable oils, and little used for lubrica- 
tion. 

58. Lard Oil is the most extensively used of all the animal 
oils, and is an excellent lubricant, although inferior to sperm- 
oil. It is obtained from the fats of the hog. It is exported 
from the United States to Europe in large quantities for the 
purpose of adulterating olive-oil. It is itself often adulterated 



THE LUBRICANTS. II9 

with cotton-seed oil, which latter is also used as a salad-oil, but 
sold, however, as olive-oil. All three oils are good lubricants. 
Lard from which the oil is expressed yields 62 per cent, of its 
weight, the specific gravity approximating 0.925. It saponifies 
readily, congeals at the freezing-point of water, and " flashes" 
under fire-test at about 500 F. (260 C). If sperm-oil be 
rated at unity as a lubricant under ordinary conditions, lard- 
oil will stand at 0.75 to 0.95. This oil is twice as viscous as 
sperm. Exposed to air it absorbs oxygen with far less rapidity 
than sperm-oil. 

59. Neat's-foot Oil is one of the best of lubricants, and 
has extensive use in the arts. It is obtained by boiling the 
feet, and often other parts, of cattle, and skimming off the oil 
which rises to the surface of the water. It has a very slight 
straw-yellow color, which darkens with age ; it is odorless when 
fresh, has a pleasant taste, is limpid at all common tempera- 
tures, but congeals at about the freezing-point of water. 
Its density at 6o° F. (1 5-5° C.) is 0.916. It is very frequently 
adulterated with other less expensive oils. When allowed to 
stand for any length of time, it often deposits white flakes of 
solid fats. Its low temperature of congelation makes it a 
very useful oil for out-of-door machinery. It resembles lard- 
oil in general appearance and qualities. 

Tallow Oil is made from the tallow of beeves by pressure, 
and has very similar qualities to the preceding. The tallow is 
melted, the stearine separated by slow cooling and straining, 
followed by pressing. The oil is a good lubricant, but is 
principally used in fine soap-making. 

60. Fish Oils, so called, include the whale-oils already 
described, and the oil of the menhaden and other fishes. 

Seal Oil is also often classed, even more improperly than 
the whale-oils, with the fish-oils. It is not a common oil 
in our markets, and is rarely used for lubrication, although a 
good unguent. 

Porpoise Oil is used as a watch-oil, for which purpose its 
limpidity and stability of composition well fit it. It resembles 
the best whale-oils. The " porpoise-oil " of the market is very 
generally made, not from the porpoise, but from the jaws and 



120 FRICTION AND LOST WORK. 

the " melons" of the blackfish. It does not congeal at the 
zero of the Fahrenheit scale (— i8° C). It is refined by- 
straining cold. Rusty iron placed in the bottle with the oil 
keeps it free from acid. It is very expensive. "Grampus" 
oil is even better than porpoise or blackfish oil. Dolphin Oil, 
Cod-liver Oil, Dugong or Sea-calf Oil, and the oils of the 
herring, the sardine, and other fish, have still less use in the 
mechanic arts. 

Menhaden Oil has been used by the author for the pres- 
ervation of steam-boilers out of use for long periods of time, 
with very satisfactory results. It forms an impermeable and 
almost unchangeable greasy varnish, which protects the iron 
from oxidation very thoroughly. 

All these oils, like the animal oils, generally dissolve to 
a certain extent in alcohol. They are usually extracted by 
maceration and pressure. 

61. The Vegetable Oils are obtained from the seeds, and 
occasionally from the fleshy part of the fruit, of plants. In 
one case, that of the earth-almond, the oil is found in the 
woody tissue of the root. These oils are usually limpid, but 
sometimes are so hard as to be properly classed as greases. 
The oils are expressed by grinding the seeds, adding water, 
and finally treating the emulsion of water, oil, and albuminous 
matter to separate the oil. 

The vegetable oils are divided into two classes, the fixed 
or non-drying, and the drying oils. The former are permanent 
liquids, like the animal oils; the latter are subject to a process 
of oxidation which causes their gumming, and the formation 
of a resin which is useful as a kind of varnish, and as a vehicle 
for holding colors in painting. The drying-oils, among which 
the best known are linseed, castor, hemp-seed, walnut, and 
poppy oils, are of little value for purposes of lubrication. 
Castor-oil, when fresh, is a moderately good lubricant for 
heavy pressures, although the fixed oils are vastly better for 
common use. It changes much more slowly than linseed-oil. 

The non-drying oils, of which the principal are olive, cotton- 
seed, almond, rape-seed, cocoa-nut, pea-nut or ground-nut, 
and colza, are all good lubricants. Of these the first named 



THE LUBRICANTS. 121 

is by far the best known ; although cotton-seed, pea-nut, and 
colza oils are also extensively used. 

The gain in oxygen and the loss of the hydrocarbons in 
eighteen months, by the process of " drying," is thus shown 
by analyses made by Cloez : 

Linseed Oil. 

Fresh. Aerated. 

Original weight. Per cent. Total weight. Difference. 

C 77-57 67.55 72.299 - 5.271 

H 11.33 9.88 10.574 — 0.756 

O n. 10 22.57 24.157 +13-057 

Castor Oil. 

C 74-36i 72.125 74.058 — 0.303 

H 11.402 11. 108 11.405 — 0.003 

o '.. 14.237 16.767 17.217 + 2.980 

62. Olive Oil is obtained from the fruit of the Olea Europea, 
one of the jasmines, which grows throughout Southern Europe 
and Northern Africa, and in other semi-tropical countries. 
The total production of the world is vastly less than the nomi- 
nal sale, the commercial oil being adulterated to an enormous 
extent. It is extensively used as a table-oil, as well as for 
illuminating and lubricating purposes. The finer grades of 
fruit are harvested by hand-picking, and reserved for the 
manufacture of table-oils. The larger varieties of olive furnish 
the less excellent grades of oil which are used in the arts. 
Each part of the fruit, the outer skin, the pulp, the enclosed 
seed or nut, supplies an oil of peculiar quality; but they are 
rarely separated. The oil from the pulp being comparatively 
free from stearine, remains fluid at lower temperature than 
that from the other portions of the olive, and is sometimes ex- 
tracted separately as a watch or a clock oil. 

In making olive-oil, the fruit is usually first stored about 
two weeks in bins, and allowed to ferment slightly, in order 
that the softened cells may yield their oil the more easily and 
completely. The fruit is then crushed in an " edge-roller 
mill," and the oil removed by exposing the pulp so produced 






122 FRICTION AND LOST WORK. 

to heavy pressure while enclosed in bags and under a screw- 
press. The expressed oil runs into tanks of water, and is then 
separated by skimming. The " virgin-oil " is that which first 
comes off or often that which drains, unpressed, from the 
crushed paste at the roller-mill. That which is afterward ob- 
tained is called " ordinary oil." An inferior quality is obtained 
afterward from the mixture of water and paste, which is left 
to settle in a large reservoir called "Venfer" and this oil is 
therefore called " huile d enfer-" it is used for a cheap lamp- 
oil. 

Good olive-oil is limpid, unctuous, sometimes colorless, 
but usually golden yellow or greenish yellow in color, trans- 
parent, and if fresh very slightly odorous. Its taste is sweet 
and fruity, and pleasant to the palate of many persons ; but it 
becomes disagreeable and is unpleasantly odorous when it be- 
comes rancid with age. Its density varies, according to Saus- 
sure, from about 0.92 at the freezing-point to 0.86 at the boil- 
ing-point of water. It congeals at a low temperature, deposit- 
ing flakes of stearine as it approaches the freezing-point. 
Heated, it begins to change to a darker color at about 248 F. 
(120 C), and fumes at 356 F. (180 C), without decomposing, 
however, as a mass ; it must be heated to a considerably higher 
temperature before breaking up. 

All the burning and lubricating varieties of olive-oil are 
obtained after removing the virgin-oil and finer grades of ordi- 
nary oil. They are allowed to remain stored, and are kept warm 
in tanks for some months to precipitate all foreign substances: 
they are thus easily and rapidly clarified in summer, less 
rapidly and perfectly in winter. Good olive-oil is the best 
vegetable lubricant. Exposed to air, it shows symptoms of 
rancidity in a single day. It is much more viscous than sperm, 
and less so than neat's-foot oil. The best olive-oil is, for some 
purposes, equal to sperm ; and it is even claimed to be superior. 
Good olive-oil is one of the most perfectly non-drying of all 
the oils ; it experiences no other change with long exposure to 
the air than an increase of viscosity, only slightly observable, 
according to Cloez, after a year and a half ; it is then increased 
in weight 3f per cent. 



THE LUBRICANTS. 12 7, 

63. Cotton-Seed Oil has been produced since about 1856, 
in large quantities, in the United States, from the seed of the 
common cotton-plant as removed from the " boll " by the 
" gins." It is obtained by crushing the seed and expressing 
the oil, very much in the same way as other seed-oils. It is, in 
large quantity, of a dark reddish yellow, and of a rather deep- 
yellow color in smaller masses. It has a pleasant taste, is to 
some extent a slightly drying oil, and is used in adulterating 
non-drying lubricating oils, in making soaps, and for illumina- 
tion. 

This oil is nearly as permanent as olive-oil ; Cloez exposed 
it to the air for a year and a half without observing other 
change than a slight loss of fluidity. 

The crude oil may be refined by Dotch's method by stirring 
several hours, with three per cent, of its volume of caustic-pot- 
ash lye, of 45 B., or with six per cent, soda solution of 25 to 
30 B., for an hour, at the boiling-point of the lye. Yellow, 
clear oil, of density 0.926, separates from a brown soap-stock, 
and is decanted. Forty gallons of oil are made from a ton of 
seed : this is about one half the oil contained in the seed, which 
averages about 25 per cent, oil, by weight. 

64. Rape-seed Oil is expressed from the seeds of the sev- 
eral kinds of brassica, of which Brassica napus and B. rapce are 
the principal. The seeds are pressed dry, and are sometimes 
first heated to coagulate the albumen. The crude oil is sub- 
jected to a purifying process before it is ready for the market. 
Clarification is effected either by the use of sulphuric acid, as 
in Thenard's process, or by chloride of zinc, as in that of Wag- 
ner. In the latter case a solution of the chloride, of the gravity 
1.85, is used in the proportion of 1.5 to 100 of the oil. After 
shaking, and then allowing settling to go on for some days, the 
chloride is removed and the oil cleared by passing into it hot 
water and steam. The oil is also purified by the Deutsch 
method of heating to the verge of decomposition, allowing it 
to boil some hours, and finally skimming and decanting after 
cooling and settlement have taken place. 

Rape-seed oil is of light-yellow color, peculiar taste and odor, 
and is extensively used in manufactures as well as for lubrica- 



124 FRICTION AND LOST WORK. 

tion. The English seed is said to yield the best oil. Its spe- 
cific gravity is usually 0.913 to 0.917. 

65. Colza Oil is expressed from the seeds of the wild-cab- 
bage, Brassica oleracea> and is largely used for illumination and 
to some extent for lubrication in Europe, and may ultimately 
have importance in the United States, as the plant is hardy, and 
can be successfully cultivated in North America, The oil is 
considered by some authority to be equal to olive-oil, either as a 
table-oil or for industrial purposes. It has displaced sperm-oil 
in many of its applications, and is superior to the latter for 
illumination; colza is also much less costly than sperm-oil. 

Colza-oil is reported by Stephenson* to remain fluid at a 
lower temperature than sperm-oil. It is an excellent lubricant. 
If exposed for a long time to the air, this oil thickens slightly, 
but not sufficiently to class it with the drying-oils. 

66. Palm Oil is an excellent lubricant, and one of the most 
valuable of the oils. The principal source is the district lying 
south of the Volta, on the west coast of Africa, from which 
section and from South America over a hundred millions of 
pounds are supplied annually — principally to Great Britain. 
Large quantities also come from the East, and some from 
the West Indies. It is used in manufactures, and to a limited 
extent as a lubricant. The " oil-palm" is the Elceis guineensis. 

The process of manufacture is quite similar to that of mak- 
ing the seed-oils. The nut-kernels are crushed, or the oil is 
obtained by boiling in water and skimming the oil from the 
surface as it collects. 

Oils are also obtained from several palm-nuts, as the Avoira. 
The fruit of the latter is small, yellow, pulpy, and contains a 
nut, "pit," or stone. An oil is obtained from the pulp, and 
another oil from the nut. The first is yellow, always liquid 
in warm countries, and is that usually termed " palm- 
oil ;" the second is a solid, white, butter-like fat, often called 
" palm-butter," or, erroneously, cocoa-nut butter, or cocoa-nut 
oil. It is rarely sold in the market. The first of these oils is 
that used in soap and candle making. 

* Commission of Northern Lights of G. B. A. Stephenson, 1857. 



THE LUBRICANTS. 1 25 

The palm-oil of commerce is, when cold, a butter-like solid, 
orange yellow, sweet to the taste, and of a pleasant violet 
odor. It melts at 8o° to 95 F. (27 to 35 C), accordingly as 
it is fresh or old. The liquid oil is dark yellow or orange in 
color. It saponifies readily, making a yellow soap, extensively 
used as a toilet-soap. The composition of this fat is, nearly, 
stearine 31, oleine 69, or, according to Ure, principally palmitin, 
with a little oleine. 

The palm-nut oil of Mexico, the coquito-oil, is said to gum 
very slightly and to be very economical. 

67. Cocoa-nut Oil is, properly, one of the palm-oils. The 
nut of the cocoa-palm yields two kinds of oil, the one from the 
fresh pulp of the nut, the other from the pulp after decompo- 
sition has commenced. The first and best oil is made by 
grating the fruit and expressing its milky juice, from which 
the oil is obtained by boiling and decanting after settling. 
The oil is, when cold, white, wax-like, and melts at yo° F. 
(21 C). It is composed principally of a peculiar fat, cocinine, 
with a little oleine. When fluid it is colorless ; but small 
quantities of solid fat lie at the bottom when near the tem- 
perature of solidification. 

The second grade of oil is obtained by heating the partially 
decomposed pulp in tanks of water exposed to the sun, and 
skimming off the oil as it rises to the surface. The oil is 
removed and heated to the temperature of boiling water, to 
drive out any water that it may contain, and is then ready 
for the market. It is brown, of rather rank odor, and contains 
some fat-acids, products of fermentation. This oil is one of the 
most permanent of all the vegetable oils ; eighteen months expo- 
sure to the air, according to Cloez, caused no visible alteration. 

68. Elaine Oil, so-called by Chevreul, or Oleine, is the 
light oil obtained from tallow and other hard fats, either by 
pressure or by heating, leaving the more solid part, stearine, 
behind. It can be obtained from olive and some other oils 
by cooling, to solidify the heavier fats, thus leaving the oleine 
to be expressed. The oleine from olive-oil is greenish yellow 
in color, and frees all margarine at a temperature of about 
57° F. (14° C). 



126 FRICTION AND LOST WORK. 

69. Pea-nut Oil, or Ground-nut Oil, is obtained from the 
pea-nut or ground-nut, the fruit of the Arachis hypogcea, a 
small low plant or vine indigenous and common in tropical 
and sub-tropical North America. The fruit or seed grows upon 
the root, and is enclosed, usually two kernels together, in a 
grayish-yellow, woody shell or pod. It has a disagreeable 
taste when raw, but a pleasant, sweet taste when roasted. 
The oil is used for the same purposes as olive-oil, which latter 
is sometimes adulterated with it. It is a good lubricant. The 
color is light greenish yellow, its gravity 0.916 ; it is slightly 
soluble in alcohol, and has a barely perceptible odor. It solidi- 
fies at about 34 F. (i° C.) without alteration. It is not a 
noticeably drying oil, although it thickens a little with long 
exposure to air. 

70. Castor Oil is derived from a plant, ricinus, known 
from the earliest historic times as a native of India, but which 
has been extensively distributed through the warmer parts of 
Europe, and is now well known in America. 

The oil is obtained from the seeds by the processes gener- 
ally used in making the seed-oils. The seeds are first care- 
fully cleaned, and usually moderately heated, and are then 
pressed in the hydraulic press. The refuse seed left after 
thus expressing the oil is again worked over to obtain a 
second-quality oil. The lower the temperature adopted in the 
process the better the oil. The yield is about sixteen pounds 
of oil per bushel of seed. The best oil is nearly colorless ; 
lower grades are yellow or brownish yellow ; all have a nause- 
ous taste and disagreeable odor. Castor-oil is remarkable for 
its power of mixing, in all proportions, with glacial acetic acid 
and with absolute alcohol. It is soluble in four parts of 
alcohol, 0.835 or 0.850, at 15 C. (59 F.), and mixes without 
turbidity with an equal weight of that solvent at 25 C. (77 F.). 
Its specific gravity is 0.97 to 0.98 ; it congeals at — 12 to — 13 C. 
(8° to io° F.), and becomes solid at-40 C. (-40 F.) 

The oil of the first expression is used for medicinal pur- 
poses ; that of the second for oiling leather, lubricating ma- 
chinery, and other purposes. It is better for leather than 
neat's-foot oil, since it is less liable to become rancid. It is 






THE LUBRICANTS. 12 J 

too viscous for use as a lubricant on light work. It is a non- 
drying oil also, although it thickens slowly on being long 
exposed to the air. 

71. Linseed Oil is the most familiar and important of the 
" drying-oils." It is obtained from the seeds of common flax, 
Linum usitatissimum^ by either the hot or the cold processes. 
The latter gives the best grades of oil ; the former furnishes 
larger quantities of lower qualities. The best quality is light- 
yellow, the lower grades of a brownish-yellow color ; and both 
are of great value. The oil has a peculiar odor and taste, a 
specific gravity of 0.91 to 0.94; it solidifies at —17.5 ° F. 
(—27.5° C). It is principally used in mixing paints and var- 
nishes, and in making printer's ink. Its rapid oxidation and 
formation of resin — " drying," as it is called — is its most valu- 
able property ; one which, however, entirely unfits it for gen- 
eral use in lubrication. 

72. The Mineral Oils, or " Petroleums," are the fluid, bitumi- 
nous oils obtained from many different localities,, but all hav- 
ing the same mineral origin and common characteristics ; their 
type is "rock-naphtha." They are all hydrocarbons, of the 
compositions C 2 H 4 to C 30 H 30 , and are the more fluid as 
the proportion of hydrogen increases. On the one side they 
differ but little from the soft coals, C, 4 H 10 O 4 , and on the 
other side become pure liquid hydrocarbons of low density, 
as C 24 H 24 . The solid petroleum compounds are called bitumen 
and asphalt, and contain oxygen, of which the oils contain 
little or none. These oils are of inestimable value in the 
arts, both as illuminating and as lubricating oils. By their 
cheapness and by the excellent quality of the heavier petro- 
leums, they are becoming the most generally used of all the 
lubricants, either alone or mixed with other oils. 

Springs and subterranean reservoirs of mineral oil, " coal- 
oil," or petroleum are found in proximity to deposits of 
bitumen ; and often deposits of enormous extent occur in dis- 
tricts containing bituminous coals, or in drainage-areas lying 
below such coals. Such deposits have been known for ages 
in India, in Persia, and about the Caspian Sea, and have been 
known to exist in America since its first settlement. Pennsyl- 



128 FRICTION AND LOST WORK. 

vania now supplies the greater part of the petroleum of com- 
merce. 

The oil is usually obtained by boring or " drilling" artesian 
wells, and the oil often spouts from the newly-opened well in 
enormous quantities — amounting to several thousand barrels 
per day in some cases. 

Pennsylvania petroleum is usually of greenish color ; it is 
fluorescent, and has a specific gravity of about 0.8. It yields 
on refining 75 or 85 per cent, illuminating and lubricating 
oil. Oils exceeding 0.83 in density are good lubricating oils ; 
the best have a density exceeding 0.88, or even as high as 0.94. 
The refining of the oil is a process of distillation by which the 
light oils or naphthas are separated from the heavy illuminat- 
ing or heavier lubricating oils. 

An oil which evaporates at the rate of 5 per cent, in a day 
is unfit to be used as a lubricating oil. Such oils are reserved 
for other purposes. The mineral lubricating oils of commerce 
may be divided into three classes: 

(1) Natural petroleums of considerable density, purified 
by heating and retention in settling tanks, and finally by ex- 
posure to the action of superheated steam. 

(2) Rectified Oils of similar character, further improved by 
the Cheeseborough Method of filtering, under pressure while 
hot. 

(3) " Cylinder-oils" rectified by fractional distillation and 
chemically improved. 

Of these, the first are generally considered the best ; their 
density is greater than that of the other classes, and their fire 
and flash test are higher. 

Cylinder-oils should have little or no organic oil mixed 
with them : such mixture is an improvement, if not carried too 
far, in the cases of other mineral lubricants. When the feed- 
water of engines is returned to the boiler, as when open heaters 
are used, only pure mineral cylinder-oils should be used. 

A mineral oil has also been made having a density of 32 
B. (s. g. 0.86), which contains less than one half of one per cent, 
volatile matter at 140 F. (6o° C), flashing at 380 F. (193 C), 
and burning at 420 F. (2 1 2° C). Such an oil usually contains 50 



THE LUBRICANTS. 1 29 

per cent, volatile matter, and flashes not higher than 300 F. 

(149° C). 

A good mineral cylinder-oil may be obtained with a density 
not far from 25 B., i.e., specific gravity 0.9, a cold-test approxi- 
mating to the freezing-point of water, a melting-point within 
one or two degrees Fahrenheit (or about one degree centigrade) 
higher, a flashing-point exceeding 550 F. (266 C), and a fire- 
test or burning-point considerably higher than this. It con- 
tains no acid and no alkali, but it may be dark in color, — usually 
a dark brown, — and is very viscous and cohesive. 

Pure tallow may be used, alone or in a mineral oil, for this 
work ; but it has less wearing power, is liable to gum, is often 
acid, and costs considerably more than the best oils of the kind 
above described. 

73. The Well Oils are those which principally supply the 
market. Their properties are quite variable. The gravity va- 
ries from 25 Baume to above 50 (s. g. 0.9 to below 0.78), often 
varying through this whole range in a single locality. The 
Pennsylvania oils are usually greenish in color; the Canadian 
oil is often nearly black ; that from Mecca, Ohio, is yellow ; 
and the Italian oils are straw-color, sometimes verging on red. 
These oils average C. 85, H. 15. In some cases volatilization 
occurs with great rapidity at ordinary temperatures ; in other 
instances it requires temperatures approaching a low-red heat 
to vaporize them freely. The light oils are as inflammable as 
alcohol ; the heavy oils burn with difficulty. 

Light oils are converted into heavy petroleums by the 
evaporation of their more volatile constituents or by oxidation, 
thus producing the bitumens. 

74. Shale Oils are of similar composition with well-oils, 
and undoubtedly both have a common origin in the decompo- 
sition of the vegetation of an early geological age through the 
action of heat and pressure. The reservoirs from which the 
well-oils are obtained are unquestionably supplied by drainage 
from the carboniferous rocks in which the deposits of early 
vegetation are contained. Petroleums are found in all geologi- 
cal "horizons" above the eozoic system, but are principally 
derived from the bituminous shales, which are rich in the pro- 



130 FRICTION AND LOST WORK. 

ducts of decomposition of marine plants. These shales have 
been for two centuries a source of mineral oil, which is ob- 
tained by distillation. It was first thus made in France, on a 
large scale, by Selligue in 1834; and later, " paraffine-oils" 
were made at Glasgow by Young in 1850 ; and soon this be- 
came a well-established, but not extensive, branch of industry. 
Since i860 the shale-oils have been almost wholly superseded 
by oils from flowing or from pumping wells. 

75. Refined Petroleums are most generally applied to use- 
ful purposes in the arts. The heavier unrefined or crude oils 
are sometimes used, untreated, as received from the well, for 
lubricating machinery, and some of them are fully equal to 
the best of animal or vegetable oils for this purpose ; but as a 
rule, the oil from the well must be subjected to a refining pro- 
cess before it can be safely or satisfactorily made use of for 
either illumination or lubrication. 

By refining by a process of fractional distillation, the light, 
dangerously inflammable, oils and naphthas are removed from 
the illuminating and the lubricating oils, and these last are 
separated ; the lubricating oils being too heavy for use as illu- 
minants. By chilling and pressure, the parafifine or mineral 
wax is removed from the heavy oils, and sent into the market 
for use in making candles, and for other purposes. The residue 
after distillation consists mainly of mineral tar, and contains 
the coloring matters which have come to hold an important 
place in the arts. 

The process of refining, although ordinarily one of fractional 
distillation at temperatures which are higher as the operation 
progresses, is often more effectively conducted by the " vacuum 
system/' in which, by a method similar in principle to that of 
sugar-refining, evaporation of the more volatile constituents is 
conducted in a closed vessel, nearly vacuous. The distillation 
is thus carried on at a comparatively low temperature, and the 
product is found to possess properties unattainable by the 
older method of breaking up the natural petroleums. The 
separation of the lighter naphthas and distillates being thus 
completed, the heavier distillates can be mixed if desired with 
the product, and the crude oil thus reproduced without its 



THE LUBRICANTS. 13I 

vapors. Superheated steam is used in heating, and thus all 
charring is avoided. 

The refined oils are divided by Wilson into three groups: 

(1) Natural oils of great body, which are prepared for use 
by settling in tanks at a high temperature and by ordinary 
nitration to free them from mechanical impurities, and which 
are subjected to the action of superheated steam to remove 
any volatile oil which they may contain, and to give them the 
necessary body. 

(2) The same oils, filtered again at high temperature, and 
under pressure, through beds of animal charcoal, to improve 
their color. 

(3) Pale, limpid oils, obtained by distillation and subse- 
quent chemical treatment from the tarry residuum produced 
in refining ordinary petroleum for burning oils. 

These oils are sold pure by the refiner, and are mixed, fre- 
quently with good results, by the "manufacturer" of lubri- 
cating oils. The oils of the first class are best, whether used 
pure or mixed. The finer color observed in the oils of the 
second class is usually obtained at the expense of quality ; 
their higher price has no equivalent in efficiency. The third 
class are usually inferior lubricants. When to be used for the 
cylinders of steam-engines, these oils should be as viscous as 
possible, consistently with flowing through the cups at the 
rate demanded to secure effective lubrication. Oils which are 
perceptibly volatile are dangerous, and are apt also to leave 
an objectionable residuum. 

Pure natural West Virginia oil, 29 gravity Baume, is suit- 
able for all kinds of heavy machinery, and will remain limpid in 
cold cKmates. It is preferred by many consumers to sperm or 
lard oil. Oil of heavy body, and a fire-test from 330 to 350 F., 
is adapted for railroad-car axles, heavy machinery, locomo- 
tives, or for any purpose where great heat is to be provided 
against, and for bearings where heavy weight is sustained. 
It has excellent wearing properties, and will lubricate and keep 
car-journals and heavy bearings cool when oils of a low fire-test 
would volatilize. It can be used during all seasons of the year. 
Properly refined, it is entirely free from sand, tar, and still-bot- 



132 FRICTION AND 10 ST WORK. 

torn impurities. For factory use, high speed, with both heavy 
and light bearings, and wherever the lubricator is fed to bear- 
ings by capillary attraction, it is a good lubricant. Vegetable 
and animal oils are compounds of glycerine with fatty acids. 
When they become old, decomposition takes place and acid 
is set free, and the oils become rancid. This rancid oil will 
attack and injure machinery. All animal oils contain more 
or less gummy matter, which accumulates when exposed to 
the action of the atmosphere, and retards the motion of the 
machinery. Mineral oil does not absorb oxygen, whether 
alone or in contact with cotton-wool, and cannot therefore 
take fire spontaneously, as animal and vegetable oils do. 

The consumption of petroleum or mineral lubricating oils 
is largely increasing. They are used on all kinds of machinery ; 
they are the safest and cheapest lubricators, and generally su- 
perior to animal and vegetable oils and greases. 

They are safer on account of their non-oxidizing properties 
and their high fire-test, or the great heat they will resist before 
vaporizing. They are cheaper in price, and more economical, 
saving both machinery and fuel. They are more reliable, as 
they are usually pure, and uniform in quality. They last longer 
and work cleaner, and are perfectly free from acids and all im- 
purity. They neither gum nor stain materials or the manu- 
facturers' products. 

A good lubricating petroleum has been thus made by 
refining a natural well-oil of 32 B. (s. g. 0.864) to a gravity of 
29 to 30 (s. g. 0.88 to 0.875) in winter, and to 27 or 28 (s. g. 
0.892 or 0.886) in summer. A good standard is considered 
by Wilson to be a fire-test of 550 F. (288 C). 

According to Spon, 

(1) A mineral oil flashing below 300 F. (150 C.) is unsafe. 

(2) A mineral oil losing more than 5 per cent, in ten hours 
at 6o° to 70 F. (15 to 20 C.) is inadmissible, as the evaporation 
creates a gum, or leaves the bearing dry. 

(3) The most fluid oil that will remain in its place, fulfill- 
ing other conditions, is the best for all light bearings at high 
speeds. 

(4) The best oil is that which has the greatest adhesion to 



THE LUBRICANTS. 1 33 

metallic surfaces, and the least cohesion in its own particles : 
in this respect fine mineral oils stand first, sperm-oils second, 
neat's-foot oil third, and lard-oil fourth ; consequently the fin- 
est mineral oils are best for light bearings and high velocities. 
The best animal oil to give body to fine mineral oils is sperm- 
oil ; lard and neat's-foot oils may replace sperm-oil when greater 
tenacity is required. 

(5) The best mineral oil for steam-cylinders is one having 
a density of 0.893, and a flashing-point of 68o° F. (360 C). 

(6) The best mineral oil for heavy machinery has a density 
of .880, and a flashing-point of 520 F. (269 C). 

(7) The best mineral oil for light bearings and high veloci- 
ties has a density of 0.871, and a flashing-point of 500 F. 
(262 C). 

(8) Mineral oils alone are not suited for very heavy machin- 
ery, on account of their want of body, but well-purified animal 
oils are applicable to the heaviest machinery. 

(9) Olive-oil stands first among vegetable oils, as it can be 
purified without the aid of mineral acids. The other vegetable 
oils which, though far inferior to olive-oil, are admissible as 
lubricants are, in their order of merit, sesame, earth-nut, rape 
and colza, and cotton-seed oils. 

(10) No oil is admissible which has been purified by means 
of mineral acids. 

"Mixed Oils' consist usually of mineral oils — petroleums 
of the heavier grades — mixed with some animal or vegetable 
oil, and usually probably with lard-oil. These oils, if prop- 
erly mixed, possess the special advantages of both classes. 
The mineral oil, of which the mixture generally principally con- 
sists, is free from liability to " gumming" or " drying" by 
rapid oxidation, and has also the property of freely dissolving 
the organic oils, and of holding them in solution in large pro- 
portions, thus taking a " body" which the lighter rock-oils often 
lack. The mixture is thus a good lubricant, and at the same 
time comparatively inexpensive ; it is also a safe oil. The 
petroleums so used should be the best of refined oils. The 
best animal oil for the mixture is sperm ; lard and neat's-foot 
are much used, but are not as good : the former sometimes 



134 FRICTION AND LOST WORK. 

separates to such an extent as to produce danger of spontane- 
ous combustion where the conditions are right. 

A light mineral oil, unmixed with animal or vegetable 
fatty material, will sometimes permit objectionable wear of 
bearings, even while reducing friction, to a greater extent than 
a mixed or a heavier oil having less friction-reducing power. 
The finest mineral oils may be used without mixing, however, 
except where their liability to stain goods, as in some cotton- 
mills, constitutes a serious objection. 

A mixture of paraffine and lard oils, forced between the 
surfaces by the use of a force-pump, will at low speeds carry 
the heaviest pressures met with under drawbridges. 

Mixed Greases are usually applied only to bearings sustain- 
ing very heavy pressures. They are generally made up princi- 
pally of palm-oil or tallow, with lighter lubricants to soften 
them to the proper degree of consistency, and often with water 
and an alkali to saponify them, and so to secure solubility. 
Thus the yellow fat used to grease axles on railways is a 
mixture of palm-oil and tallow, to which is added a small 
quantity of soda and some water. 

Lubricants compounded of the well-known oils and greases 
are therefore, as has been stated, very generally employed, the 
manufacturer selecting and proportioning the constituents in 
such manner as to secure precisely that set of qualities that he 
may consider best for the specific application which he may 
have in view. Nearly all the lubricants sold in the market un- 
der trade-names are of this class. This tendency is very gener- 
ally observed, and the substitution of " manufactured " oils and 
greases for the unmixed lubricants is everywhere noticeable. 
The conditions most favorable to success are not yet well- 
established, and the business of mixing is mainly directed by 
empirical methods. 

76. Purification is practised with sulphuric acid, and then 
with some alkaline base. 

The illuminating oils have a density of from 0.8 upward, and 
the lubricating oils from 0.85 to 0.88. Their boiling-points are 
from 340 to 575 F. (170 to 302 C). The former, " kerosene," 
is often unsafe from having too low a burning-point. Its cost 



THE LUBRICANTS. 1 35 

is but a fraction of that of other illuminants. An average 
Pennsylvania oil, according to Chandler, yields : 

Gasolene 1.5 

Naphtha 10.0 

Illuminating oil 55.0 

Lubricating oil 17.5 

Paraffine 2.0 

Loss, gas, coke 10.0 

1 00.0 



According to Professor J. Lawrence Smith, good " kero- 
sene" should have the following characteristics: (1) The color 
should be white or light yellow, with a blue reflection. (2) 
The odor should be faint, and not disagreeable. (3) The 
specific gravity, at 6o° F., ought not to be below 0.795 nor 
above 0.84. (4) When mixed with an equal volume of sul- 
phuric acid of the density of 1.53, the color ought not to be- 
come darker, but lighter. A petroleum that satisfies all these 
conditions, and possesses the proper flashing-point, may be re- 
garded as pure and safe. 

According to Grotowsky, the petroleums, when exposed to 
sunlight, become charged with ozone, and lose illuminating 
quality, gaining in density and become yellower in color. 
They should be protected from the action of light and air. 

Cleansing Oils which have been used is done satisfactorily 
by first storing in tanks long enough to permit settlement, next 
filtering, and finally mixing with a hot solution of 10 or 15 per 
cent, by volume of equal parts carbonate of soda and chloride 
of calcium, and a little salt, stirring well, and leaving it a week 
to settle before decanting. 

By another method a tank with an agitator is constructed, 
the tank of wood, lined with lead. Introducing 500 gallons 
of oil, the agitator is set in motion, and 26 lbs. oil of vitriol are 
added by a perforated leaden trough, so arranged as to spread 
it in a shower over the surface of the oil. The agitation 
should be continued eight hours. The oil is then allowed to 
stand ten hours, the acid is next drawn off, and the oil pumped 
into a steaming tank of iron. It is then steamed eight hours, 



136 FRICTION AND LOST WORK. 

leading in the steam through a half-inch steam-pipe. Allowing 
the oil to stand for thirty hours, draw off the water, and pump 
into receiving tanks (of wood lined with lead). The lead-lining 
should be " burned," as if soldered it is liable to fall apart. 

Filtering oils is often found decidedly advantageous. Oils 
not so purified by the manufacturer or dealer, or which have 
been used, should be carefully filtered before introduction into 
the oil-cup. Cylinder-oils of fine quality cannot, strictly speak- 
ing, be filtered : they can simply be strained through fine wire- 
netting, and should, if practicable, be strained warm (about 
ioo° F. ; 37.7 C). The best oils will pass through the 
finest nettings made. This class of oils should be filtered 
with especial care, as chips, dirt, or " still-bottom" impuri- 
ties, entering with the oil, would be likely to do serious harm. 
Oils not fed by " automatic cups" are less liable to give trou- 
ble if unfiltered ; but it is better to filter all oils not filtered 
before purchase, unless they are heavy-bodied mineral engine 
and machinery oils, which are seldom used again from the 
" drip-pans." Light oils are often used over and over again, 
and should be filtered each time. This system also permits 
that free and copious supply which will be seen later to be a 
condition of economy of power, efficiency of machinery, and 
reduction of expense. 

Filters consist usually of several thicknesses of " cheese- 
cloth," strained across the mouth of a can or bucket which 
serves as a receptacle for the oil, and from which it is drawn 
by a faucet set several inches above the bottom in order that 
any sediment that may still be precipitated may not be taken 
out with the oil. The two or three thicknesses of cloth should 
not be in contact, but should be separated by an air-space. A 
faucet at the bottom can be used occasionally to draw off the 
lower layer of sediment-charged " settlings." Filters may be 
made of successive layers of wire-netting, muslin, and other 
cloths, as flannel and hair-felt, with charcoal interposed, and 
thus an almost absolute purity of oil secured. The proper 
order is that which passes the oil through the coarsest mate- 
rials first, the finest last. The lowest diaphragm should be of 
wire, strong enough to carry all above it. 



CHAPTER IV. 

LUBRICATION— METHODS OF APPLYING LUBRICANTS. 

77. The Methods of Lubricating rubbing surfaces are as 
various as the forms of lubricants and the conditions under 
which friction is to be reduced, and their proper selection is of 
essential importance. The lubricants in solid, semi-solid, and 
liquid forms require different methods of application, and each 
is used in a different class of lubricating apparatus. The solid 
lubricants do not flow, do not wear rapidly, and are put in 
place only at long intervals ; and they remain until so greatly 
depreciated as to compel their replacement. The semi-solid 
lubricants may be caused to flow by either heat or pressure, 
and are usually " fed " to the bearing under the influence both 
of pressure and the moderate warmth which may be felt in 
nearly every pair of rubbing parts. The liquid unguents flow 
so freely that reservoirs must be provided in which they are 
stored in conveniently small quantities in close proximity to 
the rubbing surfaces, and from which by some reliable device 
they may be supplied regularly and continuously in such quan- 
tities as may be needed. In rare cases no lubricant is used, 
but the heat produced by friction is carried away by conduc- 
tion and radiation across the journal and bearing, or by a 
stream of water directed over the heated parts ; in still rarer 
cases water is supplied in such manner that it itself forms the 
bearing. 

The Method of Supply \s a matter of supreme importance. 
The "oil-bath," as shown later, sometimes reduces friction to 
one tenth the amount observed with the more common meth- 
ods. In all cases in which oil-cups are used, oil-grooves should 
be cut from the oil-hole to the farthest portions of the " brass." 
End-play should also where possible be secured. An oil-pad, 



138 FRICTION AND LOST WORK. 

as in railway practice, is better than an oil-cup, and a bath is 
much better than either. 

78. The Use of Solid Lubricants is not as common as that 
of semi-solids or liquids, but is gradually becoming more gene- 
ral for cases of extremely heavy pressure ; while they are not 
entirely out of use for even very light journals. They are 
sometimes used dry and without admixture, but oftener mixed 
with the oils. In the latter case they are applied by the meth- 
ods to be described later. 

Plumbago, or graphite, and soapstone are often used dry — 
the former in bearings, the latter in various forms of " pack- 
ing." Plumbago has been used in even the finest lace-making 
and silk-weaving machinery, as well as on heavy machines, the 
operator dusting it between the rubbing surfaces — usually when 
the machinery is stopped. It has also been introduced into 
many of the mixed greases, and into oils ; in each case for best 
effect requiring a careful adjustment of the method of lubrica- 
tion to the conditions involved in its use. For iron-planing 
machines it is found to be an excellent lubricant used on the 
" ways" on which the " table" slides in the dry form ; it is ap- 
plied by dusting it on the " V's" as they are exposed during 
the operation of the machine. 

Metaline, a solid compound, usually containing plumbago, 
is made in the form of small cylinders, which are fitted perma- 
nently into holes drilled in the surface of the bearing, which 
requires no other lubrication. Various compositions are made 
for the wide range of pressures and speeds met with in ma- 
chinery. The " anti-friction" metals, so called, all require 
lubrication, and are only of special value as being soft and 
yielding, and accommodating themselves to the form of the 
journal without danger arising from "cutting" or overheating: 
even if they are melted out they are easily replaced, and no 
such serious expense is incurred as where " solid brasses" are 
used. 

79. The Semi-solid Lubricants, the Greases, are applied 
in most cases by the use of " grease-cups" or " grease-boxes." 
They are always softened and rendered more or less fluid by in- 
crease of temoerature, and are thus either caused to flow spon- 



METHODS OF APPLYING LUBRICANTS. 1 39 

taneously, or are rendered soft enough to flow under the ap- 
plication of moderate pressure. In some cases they are laid 
directly upon the rubbing surfaces, either through holes made 
for the purpose in the " caps" of the journals, or by placing 
the unguents at intervals upon parts of that surface which are 
periodically exposed. As a rule, harder and less fusible greases 
are used in summer than in winter, the difference being pro- 
duced by the adoption in mixtures of a larger proportion of 
the hardest constituents in summer and a smaller proportion 
in winter, as is illustrated in the compositions given already 
(Art. 53). 

80. The Methods of " Oiling," or of applying the fluid 
lubricants, are usually practically the same for all kinds of lubri- 
cants. On very slow-moving parts, when the pressure is mod- 
erate, the application of the oil by hand at long intervals 
suffices ; watches are often kept in good running order if oiled 
but once in two years or more. Fast-running machinery must 
be frequently oiled, and is generally and should be always so 
arranged that the supply may be made continuous. In excep- 
tional cases special provision — as by oil-pumps — is made to 
secure certainty of continuous and liberal supply. The most 
usual method of continuous lubrication is by the use of " oil- 
cups" — small metal or glass reservoirs mounted generally upon 
the piece to be oiled, and supplying the oil through a small 
channel along which it is " fed " by some device, bringing into 
play capillary action, as by a wick or by a loosely-fitted wire 
in the manner to be described presently. 

Economy is best secured where the dripping oil is not pre- 
served by any arrangement which furnishes the lubricant in a 
perfectly uniform supply and in minimum safe quantity. In 
some cases " self-oiling" boxes are used with good results; in 
these arrangements the oil is contained in chambers or reser- 
voirs in close proximity to the rubbing surfaces, and in suffi- 
cient quantity often to require renewal only at intervals of 
several months. Where this system involves the oil-bath, it 
is probably best of all. Careful management of the ordinary 
system of oiling with the common oil-cup will, however, give 
equal economy of oil : the line-shafting of a large machine- 



I40 FRICTION AND LOST WORK. 

shop has been kept running for long periods of time with an 
expenditure of but 17 drops of sperm-oil per bearing per week. 
The reduction of friction is not as effective, however, as in the 
preceding case. 

Uniformity of distribution is as important as uniformity 
and continuity of supply. A dry spot occurring on the jour- 
nal will immediately cause heating and " cutting." The oil 
should therefore be led upon the journal in such a manner as 
to insure that every part shall be reached and kept well lubri- 
cated. The method of oiling, as well as the quality and kind 
of lubricant, should be adapted to the special case in hand. 

Since the lubricant is not itself worn, and undergoes no 
physical change while in use, and no other chemical change 
than that of gumming by exposure to air, a flooded journal 
with an effective system of collecting and reapplying the out- 
flowing oil, with occasional purification as may be necessary, 
gives maximum economy both of power and of lubricant. 

Steam-cylinder lubricants are best supplied by the " auto- 
matic" feed-cup, of which many varieties are made, and among 
which some few serve their purpose admirably. The form 
used for this purpose should be capable of supplying the heav- 
iest and darkest of mineral cylinder-oils, and with perfect uni- 
formity and certainty at minimum rates of flow. The " sight- 
feed " cups, in which each drop of oil is seen as it passes from 
the reservoir through a glass feed-tube to the steam-pipe, is a 
form which has the double advantage of doing its work well, 
and of at all times doing it in view of the attendant. The cup 
used should be as carefully kept in order as the engine itself. 
The rate of feed is usually made a minimum, and with good 
lubricants can be reduced to 4 or 5 drops per minute per 100 
horse-power of engine, and perhaps somewhat lower still with 
engines of more than 100 horse-power. 

Mineral cylinder-oils, when used after the habitual use of 
animal or vegetable oils, will gradually dissolve the gum 
already deposited in the cylinder and its passages, and will 
later work well and keep the cylinder clean. Some loss of 
efficiency may be noticed in the interval. If the gum is 
thrown off in masses, as sometimes happens, it may give 



METHODS OF APPLYING LUBRICANTS. I4I 

trouble ; and it is much better to carefully inspect the cylinder 
and remove any that may exist before danger can arise. This 
process may occupy weeks, and is a particularly slow process 
after tallow has been long used. 

Lubricants used in bolt-cutting demand the same qualities 
as for other cases of lubrication, and in considerable degree 
their choice is similarly determined. That oil which will give 
the smoothest cut and finest finish with minimum expendi- 
ture of power is cheapest as a rule, whatever may be the 
market price. The best lard-oil is commonly used for this 
purpose ; mineral oils are also used. 

Recent investigations show that, contrary to earlier opinions, 
the best method of using oil, and particularly on fast-running 
machinery, is to supply it as freely as possible, and receiving 
the rejected portion, reapply it after thoroughly filtering it if 
necessary. 

The heavy mineral oils only should be used in steam-cylin- 
ders and on hot rubbing surfaces. The best of animal and 
vegetable oils will decompose, and will corrode metal so rapidly 
as often to cause serious expense, even where they might be 
otherwise desirable unguents ; their fatty acids are dangerous 
constituents, and their liability to gum is a source of danger 
as well as of expense. 

In textile manufactures the relative value of oils and ex- 
pense of operating is influenced to an important extent by the 
greater or less liability of the oils used staining the fabrics 
made, and this consideration alone will often determine a 
choice of oils without regard to price. 

81. The Forms of " Grease-Cup," or of " tallow-cup," 
used in applying the semi-solids and the more fluid greases 
are usually all of one class. A reservoir, box, or cup is placed 
in contact with the bearing to be lubricated, and is filled with 
the grease, tallow, or other semi-solid unguent : the lubricant 
settles down gradually upon the bearing, through an opening 
of usually quite large section ; or it is forced through a smaller 
passage under the pressure produced by a weight or a spring. 
In some cases the reservoir is formed in the " cap" of the bear- 
ing, and a slot cut down through the cap allows the unguent to 



14- 



FRICTION AND LOST WORK. 



settle down slowly upon the journal : with soft tallows and 
greases this provision is ample, and the stored lubricant is only- 
drawn upon when the bearing is at that temperature which, if 
the adjustment is correct, gives at once minimum friction and 
maximum economy. 

Grease-cups similar in form and in method of attachment 
to the common oil-cup are sometimes used, as in the figures, 
which illustrate the construction of two such cups. 

The first form of cup (Fig. 20) is placed in the vertical posi- 
tion, and the weight of the piston and of any material with 
which it may be loaded forces the grease into the oil-channels. 





Fig. 20. — The Weighted 
Lubricator-cup. 



Fig. 21. — The Spring 
Grease-cup. 



The body of the cup is of glass, and permits the flow of the 
grease to be conveniently watched. When first applied, the 
unguent is forced into the journal by pushing down the piston 
a little way by hand. The second style of cup (Fig. 21) is set 
in any convenient position, and the " feeding" is accomplished 
by giving the cap a slight movement by hand once a day or 
once a week, according to the character of the work. Forms of 
cup are sometimes used in which the movement of the piston 
in the first-described grease-cup is effected by a screw. 

With journals not covered by " pillow-block caps," these 
contrivances are not needed : the grease or tallow is laid 
directly upon the journal, and if sufficiently hard and cohe- 
sive, works satisfactorily and with economy. 



METHODS OF APPLYING LUBRICANTS. 



143 



82. The Forms of Oil-cup in common use are very sim- 
ple in construction, and are, if properly adjusted to their work, 
economical. Whatever the form of cup, if the flow of oil can 
be made uniform and in minimum quantity consistent with 
safety, and with perfect certainty of continuous supply, maxi- 
mum economy can be attained. 

The most common form of oil-cup consists of a small metal 





Fig. 22. 



Needle Lubricators. 



Fig. 23. 



or glass vessel or vase fitted with a central tube rising nearly to 
its top, and opening downward into the oil-hole, into which the 
supporting stem of the cup is screwed. " Wicking" is twisted 
into a loosely laid-up cord, which is entered into this vertical 
tube, one end hanging down below the level of the bottom of 
the oil-cup, the other lying over the top of the feed-tube, and 
dipping into the reservoir of oil. The Author has sometimes 
coiled such loose strands of wick loosely about a bent wire, 
one end of which dips into the cup, the other into the feed- 
tube : this can be removed when the machinery is at rest, and 
replaced before starting ; thus, in the operation of marine or 
other intermittently operated engines, effecting an- observable 
economy. 

The " Needle Lubricator" (Figs. 22 and 23) consists of a 



144 



FRICTION AND LOST WORK. 



reservoir fitted with a central delivery-tube, terminating a little 
above the bottom of the reservoir, and itself nearly filled with 
a loosely-fitted wire, the lower end of which reaches down to 
and rests upon the journal to be oiled, while the upper end 
rises into the mass of oil with which the cup is filled. 

There is no flow of oil while the machinery is at rest. 
Being perfectly air-tight, the oil will not gum. The size of the 
wire is reduced if the oil is desired to " feed " more rapidly. 
As the flow is produced by the vibration of the shaft and con- 





Fig. 24. 



■Elevation. Fig. 25. 

Seibert Sight-feed Oil-cups. 



-Section. 



sequent jar of the wire or " needle," the rate of feeding is to a 
certain degree self-regulating. When the machinery is stopped, 
capillary attraction prevents flow, and there is no waste of oil. 
When lubrication is to be secured in steam-spaces, as in the 
valve-chests and cylinders of steam-engines, special forms of 
oil-cup are used, which are often called " self-acting lubricators." 
In these, the cup is provided with a central tube, which rises 
nearly to its top, and which has on one side a hole through 
which the oil may find its way into the tube and down into 
the chamber to be lubricated. A screw-cap is fitted air-tight, 



METHODS OF APPLYING LUBRICANTS. J 45 

The oil is introduced, the cap screwed firmly down, and the 
cock below opened to permit free communication with the 
steam-space. Steam fills the cup at full pressure ; as it con- 
denses the water falls drop by drop to the bottom of the cup, 
each particle displacing a drop of oil, which flows through the 
hole into the central tube, and down into the steam-chest. 
Such an apparatus has been found sometimes to reduce the 
expenditure of oil to one fourth, and even, in exceptional cases, 
to one tenth the amount used with ordinary hand-supply. 

In some cases, as illustrated above (Fig. 24), a glass gauge is 
attached, to show the level of the surface of contact of the oil 
and the water; and in other cups a pipe leading to the main 
steam-pipe, to furnish a means of securing a more rapid flow of 
oil if needed. 

These instruments are sometimes called " hydrostatic lubri- 
cators." Such lubricators are often so arranged that the oil 
may be seen rising drop by drop through water, as in Fig. 24, 
in which B is the oil-feed pipe to the engine, D the cup, E the 
glass " indicator" up which the oil rises, F the condenser sup- 
plying water by condensing steam. This forms what is often 
called a " sight-feed " cup, or lubricator. 

Another cup (Fig. 26) has a similar general arrangement. 
E is the steam connection, AJ the cup, D a glass water- 
gauge which shows water when the oil is low, and the feed- 
chamber has a guide, as shown, to direct the drop. 

The automatic " sight-feed" lubricating apparatus is usually 
much more economical than any "hand-feed" can be, and in 
some cases has been known to save nearly one half the oil de- 
manded by the latter method on railway passenger-trains, and 
a third on freight-service. It should preferably be placed be- 
tween the throttle-valve and the boiler. 

Feed-cups for steam-cylinder lubrication are best when so 
constructed that the drops can be seen plainly and as far away 
as possible. The drop should be cut off squarely, and at 
exactly equal intervals. The larger the drop, as a rule, the 
better, and the more certain is it to flow with regularity and 
certainty with the best and heaviest oils. 

One of these lubricators is shown in Fig. 27 as attached to 






146 



FRICTION AND LOST WORK. 



the steam-pipe by the steam and discharge pipes, A and B. 
Steam condenses in F, filling it and displacing the oil in D y 
which flows up through E to the steam-pipe and the engine. 
S3. Machinery in Rapid Motion, and especially rapidly 



SIGHT FEED 




Fig. 26. — Craig Automatic Sight-feed Lubricator. 

revolving parts, are sometimes very difficult to lubricate. The 
crank-pins of fast-running steam-engines are examples of such 
cases, in which also perfect lubrication is of vital necessity to 
the successful operation of the machine. In such cases special 
devices are often adopted. One usually satisfactory but some- 



METHODS OF APPLYING LUBRICANTS. 



H7 



what costly device is that of drilling oil-passages from the body 
of the shaft out, through the crank, and then into the pin, 
finally leading the oil out laterally to its surface, thus taking 
the oil in at a point which is comparatively accessible, and tak- 
ing advantage of the action of centrifugal force to carry it 
forward to the surfaces to be reached. Overhung pins are 
often fitted with a lubricating device consisting of an ellipsoidal 




Fig. 27. — Sight-feed Attached. 



or spheroidal oil-reservoir placed in the line of the axis of the 
shaft, and carried by a tube connecting it to the end of the 
crank-pin. The oil is introduced, in any convenient manner, 
into an opening at the axis of the reservoir, and finds its way 
outward through the carrier-tube and thence into the pin and 
to its rubbing surfaces. The Common oil-cup is often used as 
a feeder to the reservoir. Another method (Fig. 28) is that 
adopted by Messrs. Armington & Sims. 



148 



FRICTION AND LOST WORK. 



84. Oiling by Hand is practised both in lubricating rub- 
bing parts easily kept in order, and oftener in filling oil-cups at 
intervals, and renewing their contents as expended. The com- 
mon hand " oil-can" is a reservoir usually of brass or tin fitted 
with a spout from which the contained oil maybe conveniently 
poured in as small quantities as may be desired. It is made 
large enough to hold as much as it is found convenient to carry, 
and is principally used to supply smaller receptacles and oil- 
cups. 

The " Oil-feeder," or " Oil-can," or " Squirt-can," as it is 
variously called in the shop, is a conically-shaped vessel, small 
enough usually to be carried conveniently in one hand, which 




Fig. 28.— Crank-pin Lubricator. 



has a flexible and elastic bottom ; while at the upper and 
smaller end of the cone a tapering tube is screwed which has 
a very small orifice at its extremity. This little instrument 
being filled or partly filled with oil, held between the middle 
fingers and inverted, the pressure of the thumb on the bottom 
causes the oil to spurt from the point of the tube in a fine jet r 
which is directed to the point at which the oil is needed. 

85. " Oil-Pumps" are sometimes used where the bearing 
to be lubricated is either peculiarly important, as the steps of 
vertical shafts or the " thrust-bearing" of a steamship, or where 
it is unusually liable to heat. In such cases a reservoir of consid- 
erable volume is placed in a convenient location and nearly filled 
with oil, a pump connected by its suction-pipe with this reser- 
voir, and by a force-pipe with the bearing, is kept in operation 



METHODS OF APPLYING LUBRICANTS. I49 

by connection with the mechanism to be oiled, and an ample 
and continuous supply is thus secured. Even this arrangement 
is liable to failure, and to cause the very accident that it is 
intended to prevent if the oil used is not absolutely free from 
foreign material, if the connections are not ail well made, if 
the valves of the pump leak or fail to seat properly, or if the 
pump-plunger is not kept well packed. 

86. Water-Bearings have been adopted in some cases, as 
by Shaw and by Giffard, — the " pollers glissants" of the French 
engineers, — in which the weight of a revolving shaft is taken 
by a cushion of water, or sometimes of oil, and in which the 
journal does not bear upon metal at all, except as it may be 
necessary to steady it. The journal enters a bearing so con- 
structed that the liquid can be forced between the two adja- 
cent surfaces in such quantity and under such pressure that 
the journal is supported by and turned upon the fluid cushion 
so formed. The excess of the liquid which flows out at the 
end of the bearing returns to the reservoir below, and is again 
circulated by the pump. Journals thus arranged have been 
known to work many months without appreciable wear, and 
even without discoloration of the liquid. 

87. Unlubricated Bearings, cooled usually by the flow of 
water across them, are sometimes found preferable to any 
other device for sustaining parts having relative motion under 
pressure. Thus the " stern-bearings" of screw-steamers are 
almost invariably fitted up in this manner. The screw-shaft 
of iron or steel is encased in brass and turns within a long, 
hollow, cylindrical sheath, which is fitted with narrow strips of 
lignum-vitae, separated by longitudinal spaces forming water- 
channels. No lubrication is employed, and the bearing is kept 
cool by the flow of water between the strips of lignum-vitae. 
Such bearings wear well in clear water, but cut away rapidly 
in shallow water over sandy bottom. The lignum-vitae if kept 
cool will sustain enormous pressures, and will wear in such 
situations better than metal. 

88. Bearing Surfaces are of bronze or other alloys, of 
cast-iron or other metal, or of wood, according to location, in- 
tensity of pressure, velocity of rubbing, and nature of the 



I50 FRICTION AND LOST WORK. 

material of the journal. Ordnance bronze wears well under 
heavy pressures and at high speeds if not subjected to intense 
localized pressures by the springing or misfitting of parts ; 
cast-iron has an advantage, if used under moderate pressures 
and in ample extent of surface, in its porosity and absorptive 
power and the persistence with which oil and grease adhere to 
it ; wrought-iron and steel sustain heavy loads, if free from sur- 
face defects ; " mild steel " is peculiarly valuable for journals, 
and hard steel ground to shape and well bedded in its bearing 
will safely carry pressures of enormous intensity ; wood is only 
used in special cases. Too high a polish on the harder surfaces 
is objectionable where thin oils and heavy pressures are 
adopted, as the lubricant is difficult to feed between the 
metals in contact, or to keep there while in operation. 

It is nearly always advisable to make the bearing of the 
softer metal, since its renewal is a matter of less difficulty and 
expense than that of the journal, and since the journal must 
usually have great strength. A hard bearing cuts the softer 
journal, and gives rise often to serious expense. It is from 
this consideration that bearings are often " babbitted " or lined 
with the soft white alloys. 

The fitting of the surfaces in contact is as important a 
matter as the selection of the material of which they are com- 
posed. The theory of friction is based upon the assumption 
that all parts are accurately made to correct dimensions, and 
exactly fitted ; and the conclusions derived are therefore in- 
validated by any departure from such assumed conditions. 
Precision and stability of form — stiffness of all loaded parts — 
are essential elements of successful working. Stability of form 
is dependent upon extent of surface exposed to wear : if this 
area is ample, so that the two rubbing parts nowhere and at 
no time come into unrelieved metallic contact, no appreciable 
wear will occur, and their forms will be permanent. 

Surfaces of similar area and form, even when well fitted, if 
of different materials will wear very differently. Thus the 
following table shows the comparative wear of axle-bearings. 
Thoroughly pure bronzes, like those fluxed with phosphorus, 



METHODS OF APPLYING LUBRICANTS. 



151 



were reported as wearing very much less than ordinary com- 
positions. 





Composition. 


Cost 
per 

100 lbs.* 


Miles 

run 

per lb. 


Wear 
per 


Bearing. 


Cop- 
per. 


Tin. 


Anti- 
mony. 


100 miles 
for four 
bearings. 


Gun metal 


83 

82 

3 
5 

82 


17 
18 
90 

85 

18 


7 
10 


$28 60 
28 68 
32 85 
32 27 

13 04 

28 68 


25,489 
27,918 
22,075 

24,857 

22,921 
2,576 


200grs.f 
252 " 
366 •'« 

284 " 

308 " 
274 " 


< < < < 






Lead Composition: lead, 

84; antimony, 16 

Gun-metal on brake-cars . . 



In many cases the excessive wear of a bearing is due to a 
misfit. The Hopkins bearing is a bronze bearing lined with a 
thin layer of lead, which, when new and unfitted, can accom- 
modate itself to the distorted journal and permit gradual wear 
to a correct fit without danger of injury, such as occurs often 
with the common hard, unlined " brass." In the Defreest 
bearing a thin bronze bearing-piece is sustained by a strong 
iron backing-piece, and between them is a sheet-lead filling. 
Journals should be fitted without the use of emery or other 
gritty grinding material, which may adhere to its surface and 
thus produce injury. 

Bearing Surfaces of Wood are, under the conditions already 
described as favorable to their use, exceedingly durable, and 
will carry enormous loads without abrasion. Thus lignum, 
vitae will sustain pressures exceeding 1000 lbs. per square inch 
(70 kgs. per sq. cm.), where brass becomes rapidly abraded and 
destroyed under but little more than one fourth of that load, 
and will run continuously under 4000 lbs. (281 kgs. per sq. 
cm.) when bronze sets fast instantly. Camwood has been sub- 
jected to pressures exceeding 8000 lbs. per square inch (562 
kgs. per sq. cm.), and has worked without injury ; snakewood 
carries about as heavy a load as lignum-vitae. 



* Including melting expenses, loss, etc. These figures are constantly 
varying. 

f Seven thousand grains per pound. 



152 FRICTION AND LOST WORK. 

The bearing surfaces of watch-work are often made of 
ruby, agate, and other fine-grained and hard stones, and of 
gems. 

A comparison made by the author between surfaces of 
gun-bronze, of " Babbitt"-metal, and of other soft, white alloys, 
all working on steel, proved all to have substantially the same 
friction. In other words, the coefficient of friction was deter- 
mined by the nature of the unguent and not by that of the 
rubbing surfaces, when the latter are in good order. The soft 
metals, however, heated more than the bronze, running at 
temperatures somewhat higher with equally free or even freer 
feed. To retain the temperature at 135 F. (57 C), in some 
cases one half more oil — over 300 grammes, as against 200 — 
was needed on the white metal than on the bronze. This 
probably does not, however, necessarily indicate a serious de- 
fect, but simply deficient conductivity. Lined journals may 
be expected to run normally warmer than unlined bronze of 
good quality. The following are the results of experiment 
with a " Babbitt"-metal, which was compared with bronze and 
a second white alloy: 

Bronzes. White Metal. 

No. 1. No. 2. 

Mean Temperature, Fahr 133 152 137 

Mean Coefficient of Friction 0.010 0.013 0.010 

Oil used per hour, ounces 7 17 .12 

These differences prove ordinary lubricated surfaces to 
have contact, since they give differences in the values of / 
where none could exist were the friction fluid-friction solely. 



CHAPTER V. 

THE INSPECTION AND TEST OF LUBRICANTS. 

89. Systematic Methods of Examination of Lubricants 

are always necessarily adopted by large consumers of lubri- 
cants. The opportunity for adulteration is so great, and a mis- 
take in purchasing is so liable to result in serious accidents and 
large expenses for repair, or for wasted driving-power, that 
very considerable expenditure of time and money is often jus- 
tified in the endeavor to secure reliable determinations of the 
quality of the unguent which it may be proposed to use. 
These methods of test are often physical, sometimes chemical; 
and very frequently they consist of direct methods of deter- 
mination of the value of the oil in reducing friction, and of 
its durability under wear and under the conditions of every- 
day work. 

Of these tests the simplest is the measurement of the den- 
sity of an oil; any variation from that of known pure oils of the 
same nominal grade being evidence of adulteration or of prob- 
ably low quality. The method to be described as " oleography" 
is another physical test, and the so-called " fire-tests" are other 
illustrations of this class. The chemical tests are usually pro- 
cesses of qualitative analysis, and the last-mentioned systems 
of test are generally practised by the use of "testing-machines," 
forms of which will be described later. 

The density of the oils is always less than that of water, 
and varies from 0.875, tnat °f sperm-oil, to 0.99, that of 
the heaviest rosin-oils. The gravity of the oil, except per- 
haps in the case of sperm, is not a definite gauge either of the 
nature or of the quality of a lubricating oil, as mixtures may 
be made of any desirable density. There is also no direct re- 
lation between their lubricating property and their density. 



154 FRICTION AND LOST WORK. 

The determination of density is therefore an aid simply, and 
not a real test of quality 

The Color of an oil is a noteworthy characteristic of a pure 
oil, but is so readily imitated and so frequently purely the 
result of accident, that it cannot be assumed to be a reliable 
guide in selecting lubricants. The best oils are, however, usu- 
ally either colorless or very slightly yellow : a few are brown- 
ish or brownish red, and olive-oil has a slightly greenish tint. 

The Odor of oils is due in the case of the animal oils to 
the presence of a volatile compound, generally acid, as butyric,, 
valeric, or other fatty acid, and in the hydrocarbons to vola- 
tile vapors, as naphtha. The vegetable oils are often distin- 
guished by odors peculiar to the plants from which they are 
obtained. 

The Fluidity of the oil is not only very different in different 
cases, but is very variable with change of temperature. It is 
quite independent of density. 

90. The Detection of Adulteration is the principal ob- 
ject of the tests of unguents. The most valuable of the oils r 
as sperm and olive oils, are rarely found in the market per- 
fectly free from adulteration. The former is adulterated with 
blackfish and other cheaper oils, the latter with cotton and 
other seed oils ; and even the cheaper oils, as lard, are often 
mixed with cotton-seed and various inexpensive but not al- 
ways seriously objectionable oils. The lubricating oils in most 
general use are now almost invariably mixed oils ; and the 
greases are as universally made up by mixture, the character- 
istic odor of the cheaper fats being concealed by that of oil of 
almonds or other fragrant substance. It is evidently import- 
ant that the engineer should be able to determine when an oil 
or grease is pure, and to detect the nature and determine the 
extent of adulterations if it should prove to be impure. 

The modern methods of testing oils are directed to the 
determination of a number of independent facts. These ob- 
jects are : 

(1) Their identification and the detection of adulteration. 

(2) The measurement of density. 

(3) The determination of their viscosity. 



INSPECTION AND TEST OF LUBRICANTS. I 55 

(4) The detection of tendency to gum. 

(5) The determination of temperatures of decomposition, 
vaporization, and ignition. 

(6) The detection of acidity. 

(7) The measurement of the coefficient of friction. 

(8) The determination of their endurance, and their power 
of keeping the surfaces cool. 

It is sometimes sufficient for the user of an oil to identify 
it and to be able to detect adulterations. Sperm and lard oils, 
for example, are standard lubricants ; and if the consumer or 
dealer can assure himself that the oil which he has in hand is 
pure sperm or pure lard, that is often enough, since long expe- 
rience may have taught him that this oil and no other is likely 
to fully answer his purpose. 

The tests for identification are chemical and physical. The 
chemist can sometimes, by applying " reagents" which have 
peculiar effect on an oil, determine whether that oil is sperm 
or lard, or other, and detect adulterations. This is in some 
cases quite easy to do and tolerably certain, since there are 
usually very few oils of which the cost would be low enough 
to permit their use as adulterants. For example, the chemist 
would look for cotton-seed oil, perhaps, in his tests of so-called 
pure lard oil, since that, in the present condition of the mar- 
ket, is about as likely to be used as an adulterant of lard as 
any other oil. The chemical methods of test would rarely be 
used, except by an expert chemist; and it is enough to describe 
a few of the best known. 

91. Chemical Methods of Test have been proposed in 
great variety. 

Animal and vegetable oils are distinguished by the fact that 
chlorine turns animal oils brown and vegetable oils white. 
Some special tests are quite reliable for certain adulterations, 
and chemists have devoted much time to their discovery and 
to perfecting methods. 

The alkalies saponify fats and oils, and the soaps so made are 
compared in the detection of adulterations. Potash gives soft, 
and soda hard, soaps. 

The strong acids destroy the fats, altering them in very 



156 FRICTION AND LOST WORK. 

much the same manner as does the application of heat ; and 
their action is accompanied by the development of heat, the 
amount of which is an indication of the nature of the oil. The 
reactions of sulphuric and of nitric acids have been very thor- 
oughly studied. Chlorine and iodine have also been much used 
in this work. The action of the oil on metals, as on copper or 
brass, is indicative of the presence of acid in the oil ; the 
amount of this action, as evidenced by alteration of color, is a 
gauge of the quantity of acid present. Acid is not found in 
pure mineral oils. Sperm and neat's-foot oils, and tallow, are 
very often acid either from chemical alteration or from the in- 
troduction of foreign compounds having acid reactions. 

Professors Crace-Calvert, Cailletet, Chateau, Wurtz, and 
many other chemists have systematically studied the reactions 
of oils with various chemicals, with a view to their identifica- 
tion and the detection of adulteration. 

When, without any previous knowledge of the nature of any 
substance, it is proposed to discover all its constituent parts, 
and to furnish a proof that, besides the elements exhibited by 
analysis, it does not contain others, it is necessary to proceed 
with a method, and to follow strictly a systematic plan. Meth- 
ods of analysis may be numerous and of various kinds, but they 
are founded upon the same principles and all present the same 
character. In fact, in all methods of analysis certain reactions 
are made use of, which enable us to divide all bodies, or all 
those under consideration, into classes that are perfectly defined. 
Such characteristics are always made use of that each of these 
sections shall comprise, as nearly as possible, equal numbers of 
bodies which exhibit in the same degree the reactions which 
have served to establish the group. By another set of charac- 
teristics, new divisions and subdivisions are established in each 
of these classes. Proceeding in this way, a certain number of 
substances are eliminated, with which we need no longer occupy 
ourselves; and after some tests, usually but few in number, we 
acquire the knowledge that the elements of the composition 
submitted to analysis belong to such or such section or class, or 
to one of the divisions or subdivisions. 

It is only after having arrived at this result that we seek to 



INSPECTION AND TEST OF LUBRICANTS. 157 

determine by a special method the body considered, by making 
use of specific characteristics and particular reactions."* 

92. Chateau's Methodsf are among those which by gene- 
ral reactions form such classifications as facilitate the determi- 
nation of the nature of the oil, and consequently allow its 
purity to be judged. 

These general reactions are — 

(1) The use of bisulphide of calcium, giving a soap which 
remains colored or loses its color. 

(2) The colors given with the sirupy chloride of zinc. 

(3) The colors produced by ordinary sulphuric acid. 

(4) The colors produced by forming bichloride of tin. 

(5) The colors given, both cold and warm, with sirupy phos- 
phoric acid. 

(6) The colors given by the pernitrate of mercury employed 
alone or together with sulphuric acid. 

These general reactions are rendered complete by the use 
of several other reagents, potassa, ammonia, nitric acid, etc., 
the use of which will be stated in the monography of the fats. 
Finally, the nature of the oil will be ascertained with certainty 
by testing for special characteristics and particular reactions. 
The tests may be made in a large watch-glass placed on a white 
paper, on a glass plate; also on white paper, or in a small white 
porcelain capsule. In practice the watch-glass has been pre- 
ferred. 

93. Preparation and Use of the Reagents. 
Bisulphide of Calcium. — This is easily prepared by boiling 

a mixture of flowers of sulphur with chalk and water. After 
boiling a half-hour it is filtered. That which has been prepared 
several days is to be preferred. 

Chloride of Zinc {sirupy). — This reagent is prepared by 
saturating pure hydrochloric acid with oxide of zinc and 
evaporating to dryness. A sirupy aqueous solution is made of 
the product. 



* Precis d'Analyse Chemique Qualitative. MM. Gerhardt et Chancel, 
f Guide Pratique de la Connaissance, et de l'Exploitation des Corps Gras 
Industrielles. Theodore Chateau. Paris, 1S64. 



I 5 8 FRICTION AND LOST WORK. 

Sulphuric Acid (commercial and colorless). — This acid is used 
in the proportion of 3 or 4 drops to 10 or 15 drops of oil. 

Bichloride of Tin (fuming). — This reagent is obtained from 
dealers in chemicals. It is also called the "fuming liquor of 
Libavius." 

Phosphoric Acid (sirupy). — A strongly concentrated solution 
resulting from the action of nitric acid upon phosphorus, or 
else a sirupy solution of phosphoric acid prepared in advance, 
or, better still, bought of the druggist. 

Pernitrate of Mercury. — This is prepared by dissolving 
mercury in an excess of pure nitric acid. The use of this re- 
agent is twofold: 1st, in the observations of color produced by 
the salt alone ; 2d, in observations of the colors produced by 
sulphuric acid when poured over the oily mass after the action 
of the salt of mercury. 

Potassa. — Concentrated solution of caustic potassa. Chateau 
uses alcoholic potassa. 

Ammonia. — That of commerce — colorless. 

Nitric Acid (pure). — Commercial. 

All these reagents are employed by pouring a few drops 
(four or five) on the oil, which is placed in a watch-glass, cover- 
ing about half its surface. 

With the concrete oils, the fats, tallows > and waxes, four or 
five drops of the reagent are used with a piece of the fat of 
the size of a pea. 

94. The Reactions of Oils when they are subjected under 
similar conditions to the general reagents already indicated are 
given in the following tables by Chateau. 

To facilitate and guide investigation, the oils are divided 
into mineral oils, the drying and non-drying vegetable oils, and 
animal oils. 



INSPECTION AND TEST OF LUBRICANTS. 



159 



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FRICTION AND LOST WORK. 



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<; 
2 


Cod-liver 
(violet blue, 
reddish vio- 
let, violet of 
pansy, crim- 
son). 

Dragon's- 
blood. 

Ray, same. 


Q 
W 


Olive {latn- 

pante). 
Rape-seed. 
Colza. 


d 
2 

ft 


Linseed (Eng- 
lish), green 
veins. 

Linseed (N. Eu- 
rope), (bluish 
green.) 

Linseed(Bay'e), 
(bluish green.) 

Linseed (India), 
(bluish green.) 

Hemp-seed. 


O 

3 
si 

ID 

«.• 

&> 

PQ 

w . 

«3 
>> 

■j> *-< 

gm 

•a'oi 

jd 

!2 

'S 

O 

ca 


< 

2 


Neat's-foot (Buenos 
Ayres), (R.Y.) 

Horse-foot (R.Y.). 

Tallow (R.Y.). 

Whale (O.Y.). 

Sperm (purplish R. 
B.). 

Seal. 

Fish (deep R.B.). 


Q 
W 

£ 


Olive (huile d'en- 

fer), (R.Y.) 
Pea-nut (distinct 

B.). 
Camline. 
Beech (R.Y.). 
Cotton-seed, O. 

Y.(?) 


d 
2 

ft 


Linseed (Eng- 
lish), (B.Y.). 
Linseed (N. Eu- 

Linseed 

(Bayonne). 
Linseed (India). 
White Poppy 

(India), (R.Y.) 
Nut (R.Y.). 




3 
>, 

G 
<u 

2 
3 


Rs" 

to 

w y 
&O 

3 

c 
"c3 

& 
3 


►J 
<! 

S 
2 
<1 


Neat's-foot 

(Paris). 
Sheep-foot 

(F.Y.). 


Q 
W 
X 


Olive (refined), 
do. (Ordinary). 
Sesame (F.Y.). 

Sweet Almond 
(no color). 


6 
2 

ft 


Poppy (French) 
Castor. 



INSPECTION AND TEST OF LUBRICANTS. 



161 



a 

4> 

be 

Q 
e 

to 
>> 

3 

05 

"c 

V 

o 

1 c 

(D 

u 

i 5 


J 
< 

S 

Z 

< 


■a 

u 

6 

rt"SJ 


Q 


Olive, (crude) 
(dirty green.) 

Rape-seed 
(dirty green). 


6 
z 

S 


c 

V 

T3 O 
(U >- 
0) t£ 

A-* 

V-Zs 

X 


J2 

1 4> 

tuo 

c 

°£ 
J* 

« 5 
Q'5 

|1 

C OJ 

&£ 
o 

u » 

eg 

<n 

Q 

■£ 

a 

pq 


J 

1 

z 

<3 


Neat's-foot (Paris), 

(O.Y.) 

Neat's-foot (Buenos 
Ayres), (O.Y.) 

Horse-foot (O.Y.). 

Tallow (does not so- 
lidify), (R.B.) 

Whale (clear mahog- 
any). 

Sperm (O.Y.). 

Seal (R.B.). 

Fisli (dark sepia). 

Cod (dark orange). 

Ray (dark orange). 


Q 

a 

X 


Olive (ordinary), 

(O.Y.) 
Olive (huile d'en- 

fer), (R.Y.) 
Colza. 

Pea-nut (B.R.). 
Beech (distinct 

R.Y.). 
Cotton (Y.B.). 


d 
z 


Linseed (Eng- 
lish), (D.B.R.). 

Linseed (N. Eu- 
rope), (brown- 
ish gray.) 

Linseed (India), 

(R.Y.) 


Yellow, Faint yellow (F.Y.), Bright yellow 
(B.Y.). Straw-yellow. 


< 


II 
Je42 


5 

X 

d 
z 

Q 


Olive (refined), 
(bright Y.). 

Sesame. 

Sweet Almond 
(canary Y.). 

Camline (faint 
Y.). 


Poppy (French) 
White Poppy 

(India). 
Castor (faint). 





J 






c 


< 






V 
4) 


S 









z 






•M 








U 








05 










^h C 














Q 

M 




'3 
3 






„ 


£ 


f «" i^ 








5^ zfll 




ID 

'5 
u 




i 




M |5 

•a "a 9-T3 is 05 


! 




6 
z 


\ 





Q 














j j U ffi 








S w ^ 








Ji o -a 




> 




■5 c v 




6 


j 


r'l?J 






< 


> v ", o-^--- 


O 


s 


en" *e ^^> cf.~ 


> 


IS 
>> 

V 

ho 

a 
a 

o 


z 

< 






T3 








C ^~ 




& 




« ^f >H 




_o 


a 


> > 2 




>> 

e 

V 

2 


X 


^ ^ 3 

E> c o 












o 





oaO ? ^J 
a^^ w a 
O) Cu U 
















a 




t: g.a ^ 




On 


d 
z 


1 c^-2 








«■ 3 o5 S 2 

— ^ •- —05 






£ 




V 

> 


Q 








-1 J _J-~- 




>> 




05 
















'C 




^3 


J 


4j rt . 




bp 

"u5 


< 
s 


|^| 




OS 

Ih 

o 


z 

< 


> a 
^ en 






•a ^< ^. 




o . 




S^ 2 2 




~J3 




J go o 




0! 03 


a' 




o i 


M 


<_c go ."o 




o.2 


X 


8S8SS 




tn U 


£ 


5J M 1) T3 — T3 




Q^ 




V ^ Q."— ' S ^ - 








c^^Pi U 






^< >> o 








si cu o /-n 




o 
o 

o 


d 
z 






oT 


Q 


aS'-M *j 05 




S 






, 



1 62 



FRICTION AND LOST WORK. 



m 
fa 




O 


.a 




■5 


W 


Tl 


ffl 


QJ 


H 


_Q 


fa 




O 


W 




cfl 


en 


O 


£ 


o 


O 


U 


i— i 


1 


H 


fj 


U 




< 
fa 


U 

< 


& 


u 


o 


o 
m 


fa 


cu 


C) 


c/) 


u 

1 


U 
X 


1 


fx 


t— ( 




fa 




fa 




m 




< 




H 





S 

.22 

o 

s 

1-1 
o 

M 

o 

s 

a! 

o 

1h 

o 
<u 

i 

o 


< 
S 
z 


Neat's-foot 

(blackish). 
Seal. 
Fish. 
Whale 


biC/3T3 

■— ~ O 
U 


si 

u 

Pi 


a 

w 

X 

£ 


Olive (ordinary), 

(G.) 
Olive (huile d'en- 

fer). 
Colza (B.). 
Rape-seed (B.). 
Pea-nut (G.). 
Camline (G.). 
Beech (B.). 
Cotton (gray). 


d 

z 

> 

P 


Sesame (greenish). 

Linseed (North Eu- 
rope), (blackish). 

Linseed (Bayonne), 
(gray) 

Linseed (India), 

(blackish.) 

White Poppy (gray) 

Hemp-seed (green 
and greenish). 

Castor (black). 


o 
>. 

en 

•5 

■a . 

is 

is 

V o 
be >> 

it 
6-1? 

"o 
O 

& 

*a3 


-J 

< 

z 


Neat's-foot (Paris), 

B.Y.). 
Neat's-foot (Buenos 

Ayres), (gold Y.) 
Horse-foot (g'd Y.). 
Tallow (gold Y.). 
Sperm (B.Y.). 


Q 
W 
X 


Olive (ordinary). 
Olive (huile d'en- 

fer), (R.Y.) 
Sweet Almond 

(faint Y.). 
Colza (faint Y.). 
Rape-seed (faintY.) 
Pea-nut (gold Y.). 
Camline (faint Y.). 
Sesame (do.) 
Beech (do.) 
Cotton (do.) 


d 
z 

« 

Q 


Linseed (North Eu- 
rope), (B.Y.) 

Linseed (Bayonne), 
(B.Y.) 

White Poppy (In- 
dia), (B.Y.) 

Hemp-seed (R.Y.). 

Nut (B.Y. ). 

Castor (B.Y»). 


a 
,o 

V. 

o 
'o 
U 

o 


J 

< 
s 

z 
< 


o 

o 

a 

C/5 


en 

12 

rt 
CQ 

a 
& 

o • 

*i 

J3 O 
en u 

'■S-° 
"8 


Seal. 

Fish. 

Whale. 

Cod. 

Ray. 


d 

W 

X 

£ 


Olive 

(superfine) 

Olive 

(crude). 




1 


Poppy 

(French). 


1 

en 

C 

2 





en 

'3 

5 

6 

in, 
a 

<u 

<0 

z% 

en 

'5 

V 

<u 

o 
1 

en 

G 
4J 
<U 

O 


< 

s 

z 
< 




Q 
14 
X 


Olive (superfine), 

(greenish Y.) 
Olive (ordinary), 

(greenish Y.) 
Olive (crude), (S. 

G., and greenish 

Y.) 
Colza. 

Rape-seed (S.G ). 
Camline (faint G.). 


6 
z 

> 

P 


Linseed 

(English). 

Hemp-seed 
(greenish af- 
ter agitation). 


u & 

St 

^^ 

e!S 
*t 

OS 
<u >, 
>*■„ 
*± bio 

c c 
3 2 

fe - 

1! 


J 

< 

z 


Neat's-foot(R.Y.) 
Horse-foot (O.Y.) 
Whale (faint Y.). 
Seal (reddish Y.). 
Fish (G.Y.). 
Cod (S.Y.). 
Ray (faint Y.). 


Q 
W 
X 


Olive (d'enfer), 

(canary Y.). 
Rape-seed (S Y.). 
Pea-nut (faintY.). 
Camline (S.Y.). 
Sesame (O.Y.). 
Cotton (faint Y.). 


d 
z 

P 


Linseed (North 
Europe), (S.Y.) 

Linseed 
Bayonne), (S Y.) 

Linseed (India), 
(faint Y., with 
veins of dark 
Y.) 

Linseed(English), 
(faint Y.) 


C 

_o 
ca 
_o 
"o 
U 
o 
c 

o 

c 

_o 

3 

s 

H 
>> 

re 

1h 

l-l 

o 


< 
z 


Neat's-foot 

(Paris). 
Sheep-foot (W.) 
Tallow 

(no color). 
Sperm 

(no color). 


Q 

a 

X 


Sweet Almond 
(grayish white). 
Sesame (white). 
Beech (no col- 
oration). 


d 
z 

P 


Poppy (French) 

White (slightly 
yellowish). 

White Poppy 
(slightly yel- 
lowish). 

Nut (no colora- 
tion). 

Castor (white). 



INSPECTION AND TEST OF IUBRICANTS. 



163 





Z c 

°l 

2 3 . 
c/) <d 

— c 1_. 

= a u 
S § w 

CD u 

M M 

"M 

cd 

en 

5 


< 

z 

< 


5 

°— • 

SB 1) 

Hen 


. 

- CD 

H 

5 « 
hi- 

c V 

t£ 

■a cu 

II 


a 






Linseed 

(N.). 
Linseed 
(Bayonne). 
Nut. 
Castor. 


J3 

** . 

1*1 

££ 
11 

§2 
c3 


< 
< 


Neat's-foot 

(Paris), 
(chocolate B.) 
Neat's foot 
(B'nos Ayres). 

(R.B. and 

chocolate B.) 
Horse-footiB. 

R. and choc- 
olate). 
Tallow (light 
chocolate B.). 
Whale (dark 

chocolate B.) 
Sperm (light 
B.and black). 
Seal (br. bl.). 
Fish (br. bl.). 
Cod-liver 

(dark B.). 
Ray-liver 

(sepia). 


Q 
W 
X 


Olive (super- 
fine), (R.S. 
grayish). 

Olive {lam- 

Sweet 

Almond 
(light choco- 
late). 

Colza (brown- 
ish rose, 
then bright 
B.). 

Pea- nut 

(chocolate). 

Camline (R. 
B., then 
chocolate). 

Beach (light 
R.B.). 

Cotton (light 
chocolate). 




z 
> 

Q 


Linseed (N 
Europe), (se- 
pia R.B. then 
dirty Y.) 
Linseed Ba- 
yonne), (do.) 
Linseed 
(India),(R.B.) 
Poppy 

(French). 

(dark B ) 

Nut (light B., 

dark B., 

blackish B.). 

Castor (dark 

B.). 
Hemp-seed 
(dark R.B. 
without agi- 
tation). 


J*' 
pj 

</> be 

*° 
1 

en 
O 

"3 

>< 


< 
z 

<J - 


Neat's-foot 
(Buenos 
Ayres), (R. 
Y. at first.) 
Horse-foot, 
(dirty B.Y. 
at first.) 


Q 
W 
X 


Olive (ordi- 
nary), 
(R.Y.) 
Olive (d'en- 
fer), (R. 
Y.) 
Sesame 

(green 
veins, then 
O.Y.). 



z 

p 


Linseed (N. 
Europe), 
(dirty Y. 
finally.) 

Linseed 

(Bayonne), 
(R.Y.) 

Linseed 

(India), 
(dirty Y.) 

Linseed 
(English), 

(deep Y.) 

White Pop- 
py (R.Y.). 

Castor (can- 
ary Y.and 
Gold Y. 
at first). 


E ^ 

£ bo 

S3 


< 

§ 
z 

<; 


0? 

a 

<U cfl 

CD CD 


Q 
Id 
X 


Colza (duty 
flesh color, 
then fleshy 

Rape-seed 

Ob.g.). 


0' 

z 
° 


Hemp-seed 
(G.G. by 
agitation). 





164 FRICTION AND LOST WORK. 

95. The Tables of Reactions are referred to after first 
observing the indications furnished by organoleptic methods ; 
the odor, taste, color, and consistency are characteristics that 
often assist in determining the method of adulteration. Seve- 
ral cases may be presented in the analysis of oils. 

(1) Having a commercial oil the name of which is unknown 
(without label or label effaced, for example), to ascertain what 
it is. 

(2) Knowing to what class an oil belongs, but not knowing 
its name, to ascertain it. For example, knowing of an oil that 
it is a drying, fixed, or animal oil. 

(3) The name of an oil being certainly known, to ascertain 
whether it is pure or not. 

These are three questions that the chemist, the purifier, or 
even the consumer, may at any time be called upon to decide 
— particularly the last. 

First Case. — Knowing nothing of the oil, to ascertain its 
name. 

First try the bisulphide calcium as directed in the instruc- 
tions for preparing reagents. Suppose, for example, the oil 
gives a golden-yellow emulsion which retains its color. The 
oil tested may be linseed, nut, olive (fine or crude), sweet-al- 
mond, colza, rape-seed, sesame, camline, cotton, sheep-foot, tal- 
low, or sperm. If in the reaction it does not produce effer- 
vescence and evolution of sulphuretted hydrogen, it cannot be 
tallow-oil. That is eliminated. 

Try next a current of chlorine for a quarter of an hour. If 
it produces no black coloration, it is not sperm-oil. 

Try chloride of zinc. This reagent gives a green, greenish, 
or bluish-green coloration ; the table gives the linseeds of 
India, Bayonne, and North Europe, colza, camline, sweet-al- 
mond, refined olive, and the other grades of olive, cod, and ray 
oils. 

The oil tested cannot be the lower grades of olive-oil, cod- 
liver, or ray-liver: bisulphide of calcium would have identified 
them. On the other hand, it is not rape-seed, sesame, cotton, 
English linseed, or sheep-foot, as the chloride of zinc would 
have detected them. We are thus limited to the linseeds of 



INSPECTION AND TEST OF LUBRICANTS. 1 65 

India, North Europe, and Bayonne, colza, camline, sweet-al- 
mond, and the higher qualities of olive oil. 

Try sulphuric acid. Assume it gives, for example, a dark 
reddish-brown and " dragon's-blood " color. Consulting the 
tables, it is seen that such effect indicates the linseed-oil of 
different countries, and a series of fixed and animal oils which 
had been eliminated by the preceding tests. 

The oil is, therefore, linseed-oil, and it only remains to 
determine its origin. 

Thus, without using the remaining tables, the name of the 
oil supposed to be offered for test is determined. By trying 
the reactions given by the other reagents indicated, the nature 
of the oil can be still more precisely ascertained. It is evident 
that another order of operations might have been followed, 
but it is best to commence with the bisulphide of calcium. 
This reagent divides the oils into two great groups ; and we 
next proceed, using first simple then the more complicated 
tests. 

Second Case. — Having given, for example, a fixed oil, to 
ascertain its name. 

Try bisulphide of calcium. This reagent may give, for 
example, a golden-yellow emulsion, which retains its color. 
The oil can be neither olive of low quality, pea-nut, nor beech. 
It is useless to try chlorine here. 

Pass on to chloride of zinc. We may obtain, for example, a 
greenish or bluish-green color ; the oil cannot be a poor quality 
of olive-oil, sesame, rape-seed, or cotton-seed. There remain 
colza, olive, camline, or sweet-almond. 

Test with sulphuric acid. This reagent gives, say, a red- 
dish-yellow color. This eliminates colza and illuminating olive- 
oils, leaving camline, sweet almond, and fine olive. 

Apply the fuming bichloride of tin. Perhaps a light 
brownish red may appear instantaneously, and with it a thick 
mass of faint or straw-yellow color. The first reaction elimin- 
ates sweet-almond and best olive ; the second confirms the 
first. 

The oil must then be camline. Special reactions given in 
the monography of this oil will clearly identify it. 






1 66 FRICTION AND LOST WORK. 

The most unfavorable example has been selected to illus- 
trate fully the use of these agents. Had a soap been obtained 
which did not retain its color, it would have limited the 
further investigation to only four oils. In such cases the labor 
is vastly reduced. A similar process would determine the 
name of any animal oil. 

The bisulphide of calcium effects a primary division — three 
oils on one side and eight on the other. If the characteristics 
developed indicate one of the eight, the use of chloride will 
eliminate the fish-oils, leaving it to be decided whether it is 
neat's-foot or horse-foot oil. 

Third Case. — To ascertain the purity of any oil indicated. 

As an oil is only adulterated with oils less costly, it is 
usually not difficult to decide upon a limited range of possible 
adulteration. It is also evident that an oil can only be adul- 
terated with a similar oil of inferior quality, or one possessing 
very similar properties. Thus an edible oil could not be adul- 
terated with an oil of strong odor, as olive with fish, etc. It 
is true that a difference of price does not invariably limit adul- 
teration, as the price varies in different seasons, and sometimes, 
even, from day to day. Thus colza is at one time quite costly, 
while linseed is cheap, and vice versa. The adulteration of 
colza with linseed is therefore quite probable, — it is practised to 
a great extent, — -but in other seasons the contrary is the case. 

Suppose the purity of edible poppy-oil is to be tested ? 
After having noted the organoleptic indications, test with the 
bisulphide of calcium. Suppose a soap obtained which retains 
its color? All the oils giving a soap which loses color are thus 
eliminated. Without further test, an examination of the 
tables will show that the three animal oils, sheep-foot, oleic 
acid, and sperm, are also easily eliminated, these oils having 
characteristic odor and taste. The linseed-oils also have odor, 
and are not edible. The adulteration could not be with fine 
olive-oil, for it is too costly. Illuminating olive-oil has a 
characteristic taste and odor, which throws that out. Cotton- 
seed oil, by its color and taste, and the oil of sweet almonds, 
by its price, are thrown out of the question. There remain 
nut, colza, rape-seed, sesame, camline, and poppy. 



INSPECTION AND TEST OF LUBRICANTS. 1 67 

Try the chloride of zinc. Suppose a white or slightly yel- 
lowish mass be obtained? This reaction eliminates colza, rape- 
seed, and camline, leaving nut, sesame, and poppy. 

Next use sulphuric acid, which may give a reddish-yellow 
color. As the nut-oil does not give this reaction, there remain 
sesame and poppy. 

Trying the fuming bichloride of tin, it gives a faint-yellow 
coloration and a straw-yellow solidified mass. We still find 
these reactions to indicate sesame and poppy oils. It then 
becomes certain that the poppy oil is adulterated with sesame. 

Try phosphoric acid. This gives, perhaps, a faint yellow — 
orange yellow. The detection is complete, since poppy-oil 
should give a white emulsion. Lastly, try Behrens' reagent, 
which will determine the presence of the oil of sesame with 
certainty. 

These methods apply equally well to the greases as to the 
oils. 

The reactions of the oils have been studied by many chem- 
ists, among whom are to be especially mentioned, besides 
Chateau, Calvert, Prescott, Gerhardt and Chancel.* 

These reactions, for greater convenience, have been col- 
lected into a single large table for the author by Mr. L. S. 
Randolph, which table is here given. 



* Prescott's Organic Analysis. — Precis d'Analyse Chemique Qualitative. 
MM. Gerhardt et Chancel. 



l68 FRICTION AND LOST WORK. 

TABLE II.— PHYSICAL AND CHEMICAL PROPERTIES OF OILS AND 

COLOR REACTIONS. 

[Compiled from Chateau, Calvert, Prescott, and other authors.] 



Kind of Oil. 



S. G. 



Con 
sealing 
Point, 



Natural Color. 



Odor. 



Taste. 



Drving 
Quali 



Calcium 
Bisulphide. 



Almond... 
Beech-nut. 
Camline. . . 



Cod-liver 
Castor . . . 



Colza 

Fish 

Hemp-seed. 

Lard 



0.918 
0.920 
0.925 

0.930 

0.963 

0.914 



— 20° C. 

-18 C. 
-18 C. 



Below 

14° F. 



5°C. 



6°C. 



Clear straw-yel- 
low; limpid. 
Yellowish. 

Clear golden yel 
low. 

Clear yellow to 
red brown; acid 
reaction. 

Sirupy; colorless 



Limpid; clear yel- 
lowish. 



None. 

Nearly in- 
odorous. 
Peculiar. 



Fishy. 



Nauseating. 



Bland 

sweetish. 
Mild. 

Peculiar. 



Fishy. 



Mild; acrid 
after-taste 



Linseed 

Neat's-foot 



Olive 

(Refined). 



Olive 

(Ordinary salad) 



Olive 

(Huile d'enfer) 



Pea-nut 

Poppy-seed 

Rape-seed 

Sesame 

Sperm 

Seal 

Tallow, Mutton, 
Tallow, Beef.... 
Tallow, Veal.... 



0.926 

0.915 
o-934 

0.916 

0.917 

0.917 

0.963 

0.924 

0.914 
0.921 
0.875 



•25° C. 



10° c 

to o° C. 

-27° C. 

Below 

o° C. 

5° C. to 

2 C. 

4- 4 °G. 



+ 4°C 

- 3°C 

-18 C 

- 6°C 
o°C. 



Greenish when 
fresh, after- 
wards brownish 
yellow. 

Colorless, or 
nearly so. 

Gold yellow to 

brownish. 
Yellowish. 

Greenish or yel- 
lowish; thick- 
flowing. 

Greenish yellow. 



Golden yellow, 

passing to 

brown. 
Made hot it is yel 

low; almost 

colorless. 
Limpid; straw 

yellow. 

Clear yellowish. 

Yellow. 

Limpid; orange 
yellow. 



Unpleasant. 



Slight odor 
of lard. 

Strong. 

None. 

Slight pleas- 
ant or none 



Insipid. 



Strong. 

Bland. 

Mild 
sweetish. 



Very odorous 

Almost odor- 
less. 

Slightlypleas- 
ant odor. 

Disagreeable. 

Mild. 

Fishy. 



Fixed. 
Fixed. 
Fixed. 

Animal 

Drying 

Fixed. 

Animal. 

Drying 

Animal 

Drying 
Animal 
Fixed. 

Fixed. 

Fixed. 

Fixed. 



Golden yellow ; 

permanent. 
Golden yellow ; 
not permanent. 
Golden yellow ; 

permanent. 

Golden yellow ; 
not permanent. 

Golden yellow ; 
not permanent. 

Golden yellow ; 

permanent. 
Golden yellow ; 

not permanent. 
Golden yellow ; 

not permanent. 

Dark gray ; ef- 
fervesces, giv- 
ing off H 2 S. 

Permanent. 

Not permanent. 
Permanent. 



Not permanent. 



Not permanent. 



Not permanent. 



Slightly 
pleasant 
taste. 

Disagree- 
able. 

Mild. 



Walnut 



Whale 

Cotton-seed . 



0.925 
0.925 



37° C. 

37° C. 

Melts 
betw'n 
fingers. 
-18 C. 

o°C. 
i°.C. 



Hard white. 
Hard white. 
Soft white. 



Slightly greenish 
or yellowish; 
thick. 

Brownish. 

Yellow or brown: 
yellow to color- 



Decays 
rapidly. 



Decays 
rapidly. 

Nearly odor- 
less. 

Disagreeable. 



Mild nutty. 



Disagree- 
able. 
Mild. 



Drying. 

Fixed. 

Fixed. 

Animal. 

Animal. 

Animal. 

Animal. 

Animal. 

Drying. 

Animal. 
Fixed. 



Permanent. 
Permanent. 



Not permanent. 



Permanent. 

Not permanent. 
Permanent. 



INSPECTION AND TEST OF LUBRICANTS. 



169 



TABLE II. —PHYSICAL AND CHEMICAL PROPERTIES OF OILS AND 
COLOR REACTIONS— Continued. 



Kind of Oil. 



Almond. 



Beech-nut. 
Camline... 



Cod-liver 
Castor . . . 



Colza 

Fish 

Hemp-seed. 

Lard 

Linseed... 
Neat's-foot. 



White mass, 
slightly yellow 
or no color. 

Flesh rose. 

Yellowish green 
to bluish green. 

Greenish yellow 
to bluish yellow. 

Yellowish rose. 



Greenish yellow 
to bluish yellow 
Yellow to 
brown. 



Olive 

(Refined). 



Olive 

(Ordinary salad) 



Olive 

(Huile d'enfer) 



Pea-nut 

Poppy-seed 



Rape-seed 
Sesame 



Sperm 
Seal... 



Tallow, Mutton 
Tallow, Beef... 
Tallow, Veal. . . 



Chloride of 
Zinc. 



Reddish-yellow 

emulsion. 
Greenish yellow; 

bluish yellow 
White mass, 

slightly yellow 

or no coior. 

Greenish yellow 

to bluish green. 

Greenish yellow 
to bluish green. 

Greenish yellow 
to bluish green. 

Yellow to 

brown. 
White mass or 

no color. 

Yellow to 

brown. 
No color or 

white mass. 

No color or 

white mass. 
Reddish brown. 

No color. 



No color. 



Walnut 



Whale. 



Cotton-seed . 



White mass, 
slightly yellow 
or no color. 

Yellowish brown 



Dark brown. 



Sulphuric 
Acid. 



Yellow. 

Reddish brown. 
Reddish yellow. 



Violet red, 
crimson violet 
thendarkbrown 
Bright yellow, 
then reddish 
yellow. 
Green veins or 
greenish color 
Brownish black 

Green veins or 

green color. 
Red brown. 

Dark brown; 

brownish red. 

Yellow, then 

orange yellow. 

Yellow. 



Yellow. 



Yellow, then 
reddish yellow, 

Dark brown to 
reddish brown 
Bright yellow, 
then orange 
yellow. 
Green veins or 
greenish color 
Yellow to 
reddish yellow 

Brownish red. 

Dark brown. 

Yellowish. 



Pale yellow; 
when stirred a 

reddish yellow. 
Canary yellow ; 

slightly orange. 

Reddish brown. 



Brownish red. 



Reddish brown 



Fuming 

Bichloride 

of Tin. 



No color. 



Reddish yel- 
low. 

Brownish yel- 
low to reddish 
brown. 

Green to green- 
ish blue. 

No color to 
golden yellow. 

Green to green- 
ish blue. 

Deep reddish 
brown. 

Green. 

Reddish. 

Bluish green. 

Reddish yel- 
low. 

Yellow (?) 



Yellow. 

Reddish yel- 
low. 

Distinct brown 

Reddish yel- 
low. 

Greenish. 

Faint yellow. 



Purplish; red- 
dish brown. 
Brownish. 

Canary yellow; 
H 2 S0 4 deep- 
ens the tint. 

Deep yellow. 



Canary yellow; 
H 2 S0 4 deep- 
ens the tint. 

Reddish yel- 
low. 

Orange yellow 



Orange yellow 



Canary yellow. 

Reddish yellow. 
Faint yellow. 



Thickened 

Mass, from 

SnClo. 



Faint yellow. 

Yellow to brown. 

Deep sepia. 

Dark green. 

Does not thicken 

brown red. 
Brownish. 

Orange yellow. 



Orange yellow. 

Reddish yellow. 

Brownish red. 
Yellow. 

Dirty green. 
Yellow. 

Orange yellow. 



Stringy yellow 



Clear mahogony. 



Yellowish brown 



Cold 

Phosphoric 

Acid. 



Discolored. 

White. 
Discolored. 

Reddish yellow. 

White. 

Greenish. 
Reddish yellow. 
Dark green. 
Clear yellow. 
Straw-yellow. 
Yellow. 

Greenish. 

Greenish. 

Greenish. 

Straw-yellow. 
White. 

White. 

Straw-yellow 
and orange 
yellow. 

Straw-yellow. 

Distinct brown 
red. 

No color. 



White. 



Straw yellow, 
then orange 
yellow. 

Golden yellow. 



I/O 



FRICTION AND LOST WORK. 



TABLE II.— PHYSICAL AND CHEMICAL PROPERTIES OF OILS AND 
COLOR REACTIONS— Continued. 



Kind of Oil. 



Almond.. . 
Beech-nut 
Camline... 
Cod-liver . 
Castor 



Colza. 
Fish . 



Hemp-seed. 



Hot 

Phosphoric 

Acid. 



Lard 



Linseed 

Neat's-foot. 



Olive 

(Refined). 



Olive 

(Ordinary salad) 



Olive 

(Huile d'enfer) 



Pea-nut . . . 
Poppy-seed. 
Rape-seed . 



Sesame. 
Sperm . 
Seal 



Tallow, Mutton 
Tallow, Beef. ., 



Tallow, Veal. 



Walnut. 
Whale . 



Cotton-seed. 



Faint 

yellow. 
Faint 

yellow. 
Faint 

yellow. 
Dirty green 

Bright 
yellow. 

Brown. 

Blackish. 

Green or 
greenish. 

Golden 

yellow; 
effervesces 
Bright 

yellow, 
Bright 

yellow, 
Reddish 

yellow, 



Gray. 
Gray. 



Gray 

No color. 
Brown. 



Faint 

yellow. 
Bright 

yellow. 
Blackish. 

Greenish 
yellow. 

Greenish 
yellow. 



Bright 

yellow. 
Reddish 

brown. 

Faint 
yellow. 



Pernitrate 

of 
Mercury. 



Grayish 
white. 

No colora- 
tion. 

Straw 
yellow. 

Straw 
ellow. 
hite 
emulsion, 



Wh 



Greenish. 

Golden 
yellow. 

Greenish 
after 
stirring, 

No color. 



Greenish. 

Reddish 
yellow. 

Golden 
yellow. 

Greenish 
yellow. 



Faint 

yellow. 

Slightly 
yellowish 

Straw- 
yellow. 



White. 

No color. 

Reddish 
yellow. 
Pale rose. 

Rosy when 
cold, dis- 
appears 
when hot. 
No color at 
first, after- 
wards flesh- 
color. 
No color. 

Faint 
yellow. 

Faint 
yellow. 



Addition of 

Sulphuric 

Acid. 



Light 

chocolate. 
Light reddish 

brown. 
Reddish brown 
then chocolate. 
Dark brown. 

Canary yellow ; 
golden yellow 
at first. 

Dirty flesh 
color. 

Brownish 
black. 

Dark reddish- 
brown. 

Violent effer- 
vescence; choc 
olate brown. 
Reddish brown 

Reddish 
yellow. 
Raw sienna. 



Reddish 
yellow. 

Reddish 
yellow. 

Chocolate. 

Dark brown. 

Brownish gray, 



Orange-yellow 
green veins. 

Light brown 
and black. 

Brownish 
black. 

Slight choco- 
late. 

White precipi- 
tate ; brown- 
ish violet. 

White precipi- 
tate; sienna 
passing to 
sepia. 

Sudden effer- 
vescence. 

Dark chocolate 
brown. 

Light 
chocolate. 



Potash. 



Greasy yellow soap 

Thick white emul- 
sion. 



Flocculent white 
soap. 



Reddish yellow 
soap; very thick, 

Pale yellow emul- 
sion. 
Difficult to saponify 



Thick yellowish- 
white soap. 

Pale-yellow soap, 
like a precipitate 

Pale-yellowish 
soap. 

Greasy emulsion; 
not homogeneous 

Deep yellow, homo- 
geneous soap. 



Yellow emulsion, 
slightly reddish. 

Reddish-yellow 
soap. 



'range emulsion, 
changing to thick 
soap. 

iomogeneous red- 
dish-yellow soap, 
with green veins. 



Ammonia. 



Greasy yellow soap. 

White emulsion, when 
hot. 



White emulsion. 



Greenish-yellow soap, 
very thick. 

White soap, very thick; 

gelatinous when 

heated. 
Clear golden-yellow 

emulsion. 
Thick white emulsion. 



Very thick, gelatinous 
soap; very white. 

Clear-yellow soap, be- 
coming yellowish 
white. 

Thick soap; slightly 
yellowish. 

Yellow emulsion. 

Deep-yellow emulsion, 
becoming homogene- 
ous and pale clear 
yellow. 



Pale-yellow emulsion. 

Thick reddish-yellow 
soap. 



Yellow emulsion, pass- 
ing to yellow-white. 



INSPECTION AND TEST OF LUBRICANTS. \J\ 

To detect acid, dissolve a small piece of sodium carbonate 
in an equal volume of water, and introduce the solution with 
the oil to be tested into a flask, and agitate thoroughly. The 
quantity of precipitate will be a gauge of the amount of acid 
present. 

The application of the senses of taste and smell, in the test- 
ing of lubricants, to be satisfactorilv useful demands great 
familiarity with, and experience in the use of oils, and can be 
practised with satisfactory results, usually, only by experts. 
Some oils, however, are so characteristic in taste and odor 
that a novice may readily recognize them. It is always best 
to compare the suspected oil with a sample of known purity. 
The characteristic odor of an oil can be brought out more 
strongly by warming it. The taste, odor, and " feel " of the oil 
are sometimes considerably modified by the locality whence it 
is obtained, by the season during which it is prepared, and by 
the method of manufacture. 

Methods in Detail are given as follows by M. A. Re- 
mont : * 

Qualitative Analysis should be preceded by an examination 
of the organoleptic properties of the oil, the manner in which 
it behaves under the influence of heat, and of its specific grav- 
ity. If the specific gravity of the sample is below 0.900, it con- 
tains a mineral oil; if from 0.900 to 0.975, it may contain the 
most complex mixtures; but if it is above 0.975, it is certainly 
an oil of resin. 

Begin by treating the sample with carbon-disulphide, freshly 
prepared, which gives a clear solution with all oils. If oleic 
acid or a fatty oil has been mixed with alkali to raise its spe- 
cific gravity by the formation of soap, there will be a precipi- 
tate. In such case the liquid is filtered, and the residue washed 
with carbon disulphide. It may be shown to be soap by its 
solubility in water, its alkalinity, and the turbidity more or less 
marked, which is caused by an acid poured into the solution. 

The filtrate is next freed from the carbon-disulphide by 
distillation : I c.c. of the residue is mixed with 4 c.c. of alco- 

* Bulletin de la Societi chimique de Paris. — Chemical News, 1880. 



172 FRICTION AND LOST WORK. 

hoi at 85 . If solution takes place, fatty acids are present, 
pure or mixed, and an excess of alcohol is gradually added 
If after having poured in 50 c.c. the liquid is limpid or very 
slightly cloudy, which cloudiness disappears on adding a drop 
of hydrochloric acid, the sample consists of oleic acid, pure or 
mixed with resin. If the specific gravity does not exceed 
0.905 at 1 5 , the sample is pure oleic acid. If the specific grav- 
ity is higher, it contains resin. By way of confirmation it may 
be examined with the polariscope, either alone or dissolved in 
carbon-disulphide ; and if there is a deviation the presence of 
a resinous mixture is indicated. 

If persistent cloudiness is observed in the alcoholic solution 
the fatty acids contain an oil sparingly soluble in this solvent, 
and in greater quantity as the cloud appears earlier. This 
process renders it possible to detect 2 or 3 per cent, of mineral 
oil, of resin, or fatty oil in the oleic acid known as oleine. The 
turbidity produced in the alcoholic liquid resolves itself after a 
time into little oily drops, which. line the sides of the vessel 
and which can by jarring be made to fall to the bottom of the 
tube. The volume of this residue shows approximately the 
proportion of insoluble matter. 

In the usual case 4 parts of alcohol do not completely dis- 
solve 1 part of oil. A larger quantity of the latter is then 
taken and agitated with an equal volume of alcohol. After 
settling, the alcoholic solution is decanted, and evaporated in a 
capsule. The nature and the quantity of the residue give a 
clew to the nature of the mixture. 

Next submit the oil to the action of caustic soda, employ- 
ing the method of M. Dalican for the analysis of tallows. In 
a capsule of porcelain, or preferably of enamelled cast-iron, 
there are weighed about 20 grammes of oil, and heated to ioo° 
to 110 . There is then poured in a mixture of 15 c.c. soda-lye 
at 36 B., and 10 c.c. of alcohol; the mixture is stirred and 
heated until the alcohol and the greater part of the water have 
disappeared. Then 150 c.c. of distilled water are added, and 
the boiling is kept up for half an hour, when three cases may 
occur : 

(1) The oil under the influence of the alkali is merely 






INSPECTION AND TEST OF LUBRICANTS. 1 73 

emulsified, and on the addition of water it separates distinctly ; 
this indicates either a mineral oil, a resin-oil, or a mixture of 
the two. The aqueous solution is decanted off, and is mixed 
with sulphuric acid. If there is no precipitation, or if but 
slight cloudiness is produced, the sample is a pure mineral oil. 
If there is a considerable precipitate which collects in brown 
viscid drops, giving off a strong odor of resin, and soluble in 
an excess of alcohol, we have a resin-oil, pure or mixed. The 
oil is examined with the polariscope, and if it acts upon polar- 
ized light this is a confirmation of the presence of resin-oil. If 
the specific gravity is below 0.960, there is some mineral oil 
present. A test may be made by distillation if one of the oils 
is not in too small proportion. The distillation should be 
fractional as far as possible, and conducted slowly. As the 
resin-oils boil, as a rule, at lower points than the heavy mineral 
oils, it follows that, in place of having specific gravities which 
increase with the boiling-points, as happens with the heavy 
mineral oils or pure resin-oils, there are observed with their 
mixtures very abrupt transitions. The sample ought to be 
tested with tannic chloride, and if the violet coloration is not 
very distinct, the same reagent should be applied to the first 
products of distillation, since the colorable product contained 
in the resin-oils is there chiefly met with. 

(2) There is formed by the action of caustic soda a paste-like 
mass of soap, which on treatment with water and boiling for 
some time gives a clear liquid. It is diluted with cold water 
and then supersaturated with acid. The fatty acids liberated 
collect on the surface after decantation of the water, and if 
exposed to cold crystallize. A small portion is melted in a 
tube at a low temperature, and 4 parts of alcohol at 85 are 
added first, and later an excess. Here two cases are possible : 

A. If no precipitation takes place it is because the fatty 
acids are pure, which shows that the oil examined is a pure 
fatty oil, or, which rarely happens, mixed with resin. The 
specific gravity of the fatty acids may here give good indica- 
tions, but it cannot be taken at ordinary temperatures, at 
which fatty, acids are solid. They must be melted, and the 
specific gravity taken at a definite temperature. M. Baudouin 



1 74 FRICTION AND LOST WORK. 

has given a table of the specific gravities of the fatty acids of 
certain oils taken at 30 C. Except for linseed-oil, which 
marks 0.910, the fatty oils have specific gravities ranging from 
0.892 to 0.900. To reduce the specific gravities of the fatty 
oils examined to the temperature of 30 , deduct from the 
density found, calculated on the litre, as many times 0.64 
gramme as there are degrees below, or, if the temperature is 
higher, to add to the density found as many times 0.64 
gramme as there are degrees above. If the specific gravity 
indicates that the neutral oil contains resin, an attempt may 
be made to separate it, in part at least, rapidly by agitating 
5 or 6 c.c. of the original oil with an equal volume of alcohol, 
decanting after settling, and evaporating in a capsule. There 
is thus obtained a solid or semi-fluid residue in case of resin. 
Further examination is then made with the polariscope. 

B. The fatty acids derived from the decomposition of the 
soap give a precipitate if treated with an excess of alcohol. If 
it is not, redissolve by I gramme of hydrochloric acid, and if 
after some time it is resolved into oily drops, it is mineral oil 
or resin-oil. A fatty oil containing 10 to 15 per cent, of one of 
these oils is completely saponified, and yields with boiling 
water, not an emulsion, but a soap completely soluble. The 
turbidity should yield oily drops, for there are certain fatty 
acids — those, among others, of the oil of the ground-nut or 
pea-nut (arachis) — which are soluble in a small proportion of 
alcohol at 85 , but an excess of alcohol precipitates a sparingly 
soluble portion of arachidic acid in small flocks. These flocks 
may be collected on a filter, and examined as to their com- 
plete solubility in alkalies. If their melting-point is near 73 
they may be attributed to pea-nut oil. 

(3) Or, lastly, the oil on treatment with soda may give a 
paste more or less firm, which, if placed in boiling water for 
half an hour, allows oily drops to rise to the surface, which are 
due to a mineral oil or a resin-oil. After settling for some 
minutes, a part of the supernatant liquid is decanted and 
mixed with an excess of a saturated solution of common salt. 
There is produced a precipitate of soap, which is filtered off 
on cooling. The filtrate is supersaturated with an acid. If 



INSPECTION AND TEST OF LUBRICANTS. 1 75 

there is produced a slight turbidity, and if the liquid, which 
was almost colorless when alkaline, gives off an odor of fatty 
matters, we have a neutral oil mixed with a non-saponifiable 
oil. If, on the contrary, the solution was highly colored after 
filtration, and gives, when acidified, a flocculent precipitate of 
a resinous odor, the sample is a mixture containing resin. In 
these two cases the components of the mixture may be recog- 
nized by means of the operations indicated above. 

Quantitative Analysis. — If it is desired to know the elements 
attacked by alkalies, the following method is to be followed : 
If the sample has yielded bodies insoluble in carbon-disulphide, 
it is separated, and the operation is confined to the residue of 
the distillation. Let it be assumed that the composition of 
the residue is as complex as possible, containing fatty oils, 
mineral oils, resin-oils, and solid resin. 

The mixture is saponified. Into a flask closed by a stopper, 
through which passes a long tube, are introduced 20 grammes 
of the oil, and a mixture of 15 c.c. of soda at 36 B., and 15 
c.c. alcohol at 90 to 95 per cent. The flask is then set upon 
the water-bath for half an hour, and is often shaken. At the 
end of this time the whole is poured into a funnel fitted with 
a tap and previously warmed, and which is left in a stove at 
50 to 6o° until a complete separation of the non-saponifiable 
oil from the alkaline liquid has taken place. The latter is then 
decanted into a porcelain capsule, and in its stead is poured 
15 c.c. of boiling water, which has served to rinse the flask. It 
is shaken well so as to wash the non-saponifiable matter, and 
decanted anew after settling. Finally it is washed a third 
time with boiling water. The oil in the funnel is received in 
capsule and weighed. What adheres to the sides is washed 
with a little ether, and the solution is received in another cap- 
sule, which is exposed to the air till the ether has principally 
disappeared. It is then gently heated to expel the rest, and is 
weighed. 

The alkaline liquid is kept boiling for some time to expel 
the alcohol, and after cooling it is mixed with an equal volume 
of a saturated solution of common salt freed from magnesia 
"by being boiled for a few moments with caustic soda and then 



176 FRICTION AND LOST WORK. 

filtered. In this manner the soap is precipitated in firm clots, 
carrying with it the last portion of non-saponifiable matter. 
The saline solution after settling is decanted by means of a 
pipette, and neutralized with an acid. If a notable turbidity 
is produced which collects in flocks, it is due to the presence 
of resin. The flocks are collected, dried, and weighed. The 
clots of soap are thrown upon a filter, washed twice with salt 
water, the last traces of which are removed by pressing the 
mass between sheets of blotting-paper. The soap is then 
placed in a glass beaker, moistened with about 100 c.c. of car- 
bon -disulphide recently rectified, stoppered, gently shaken at 
intervals, so as not to break the clots, three or four times, and 
left to settle. After an hour or two the carbon-disulphide,, 
which is colored yellow by the dissolved oil, separates in the 
lower part of the beaker. It is decanted by means of a pipette, 
and in its place is added a fresh portion of the solvent. It is 
shaken, left to settle, decanted, and so on, till the carbon- 
sulphide runs off almost colorless. The whole is then thrown 
upon a filter and washed for the last time. A portion of this 
last washing, if evaporated upon a watch-glass, should leave 
an insignificant residue. 

The soap on the filter is exposed to the air till the carbon- 
disulphide with which it is saturated has escaped. As for the 
carbon-disulphide solution, it is distilled gently on the water- 
bath. The last portions of the solvent are expelled by blowing 
air into the flask while placed in boiling water. When cold it 
is weighed. 

The last portion of the non-saponifiable matter thus ob- 
tained should have the same appearance as the first portion. 
If it is less fluid it still contains a portion of soap. In this 
case it is again taken up in carbon-disulphide, at a gentle heat, 
in presence of a few drops of water, to hydrate the soap, 
which without this addition would again be partially dissolved. 
It is then filtered, and the washed soap is added to the princi- 
pal mass. 

The non-saponifiable oil may consist of mineral oil, resin- 
oil, or a mixture of both. The means of detection have been 
given, but a satisfactory process for their separation is needed. 



INSPECTION AND TEST OF LUBRICANTS. 1 7? 

The soap insoluble in carbon-sulphide, which lies on the 
filter, contains resin and fatty acids combined with soda. 

The separation of these substances presents many difficul- 
ties. Several methods have been published, but none of them 
gives satisfactory results. That of M. Jean consists in exhaust- 
ing the barium-soap with ether, which should dissolve the 
resinate and leave the soaps of the fatty acids untouched. It 
is difficult to avoid the partial solution of the barium-oleate. 
Substituting for the ether boiling alcohol at 85 per cent., it 
dissolves much less of the oleate, but still takes up too much. 

As far as possible the soap is separated from the filter and 
placed in a capsule. The filter is put back in the funnel and 
filled with boiling water, The solution is effected slowly, and 
it filters by degrees; it is received in the capsule where the 
detached portion has been already placed. 

The solution of soap after cooling is mixed with caustic 
soda until precipitation ceases, and is left to settle. All the 
soap of the fatty acids is deposited, carrying down with it the 
chief portion of the resinate, a part of which, however, remains 
in solution and colors the liquid strongly. The whole is 
filtered, the filtrate accurately neutralized with sulphuric acid; 
the flocks of resin deposited are received upon a filter, which is 
weighed anew after washing in water and drying at a low tem- 
perature. The soap is redissolved in a little lukewarm water 
and an excess of barium-chloride is poured into the solution 
with agitation. The clots of barytic soap are drained in a 
filter-pump, replaced in the capsule in which the precipitation 
has been effected, and thoroughly dried in the water-bath or 
the stove. The mass is then powdered, and treated with 50 
or 60 c.c. of alcohol at 85 per cent., which is kept near the boil- 
ing-point, working it up with a pestle. It is left to settle for 
a few moments, and the supernatant alcoholic liquid is then 
decanted into a vial. 20 to 25 c.c. of alcohol are again poured 
upon the residue, let boil, decanted after settling, and so on 
till a portion of the alkali which has been used leaves on eva- 
poration scarcely any residue, which happens generally after 
120 c.c. of alcohol have been used. 

The alcoholic liquids are mixed and distilled till there re- 



178 FRICTION AND 10 ST WORK. 

mains only about 50 ex. Hydrochloric acid is added to decom- 
pose the resinate, and the resin, set at liberty, floats in the 
liquids. On cooling, it collects in a solid mass at the bottom 
of the vessel. It is thrown into a capsule, melted underwater, 
and weighed after desiccation on the water-bath. 

The residue insoluble in alcohol is treated in a similar 
manner to obtain the fatty acids. 

Olive-oil is sometimes tested for purity by simply applying 
heat. 

This test is very simple, and can be performed by any one 
possessing a good chemical thermometer. About a teaspoon- 
ful of oil is put in a test-tube, and a thermometer suspended 
in the oil, which is now to be heated to 250 C. (472 F.). 
For a comparison, a second test-tube of pure oil maybe treated 
in like manner. Pure olive-oil, when heated, grows rather 
lighter in color, but most other oils, like cotton-seed, pea-nut 
oil, etc., grow darker. The latter, also, evolve a penetrating 
and disagreeable odor, but olive-oil has a pleasant smell not 
unlike strawberries. This test, devised by Merz, is considered 
worthy of a trial. 

When mixed with cotton-seed oil, the following method is 
proposed by Dr. Nickels :* 

Pure olive, or " Gallipoli," oil, as examined by a Browning 
" direct vision" or pocket spectroscope, presents a deep shadow- 
ing, or cutting-out, of the blue and violet ray, with a fine, 
almost indistinct, line in the green, and a strong deep band in 
the red. 

Refined cotton-seed oil similarly examined presents exactly 
the same appearance, but as regards the blue and violet ray 
only, the green and red being continuous. 

If we take as a standard a given stratum of pure olive or 
Gallipoli oil in a test-tube, and a similar stratum or thickness 
of the standard oil in admixture with cotton-seed, there is no 
discernible difference as regards the shadowing in the blue and 
violet ray, but an almost entire fading out of the delicate line 
in the green, and a considerable diminution in the depth and 

* Chemical News. 



INSPECTION AND TEST OF LUBRICANTS. 1 79 

intensity of the strong band in the red, consequent upon 
" dilution" or " thinning down." With 50 per cent, in admix- 
ture, the loss in intensity is considerable; with 25 per cent, 
the variation is marked and discernible. 

A suspected sample compared with and differing thus from 
the standard, and in the absence of any direct chemical evi- 
dence as to the nature of the oil in admixture, might fairly 
fall within the range of strong presumptive evidence pointing 
towards " cotton-seed " oil as the probable dilutant. 

Pure olive-oil is exceedingly difficult to secure with certain- 
ty when purchasing in large quantity, as it is often greatly 
adulterated at the point of production. It is usually very diffi- 
cult to distinguish the several vegetable oils in any mixture of 
them. 

96. Alterations of Composition occur in the animal and 
vegetable oils, with exposure to air and light and with advanc- 
ing age, which may sometimes cause some uncertainty in the 
chemical work already described. These changes are usually 
in the direction of those modifications which lead to the pro- 
duction of resins. The oils become darker, more viscous, less 
susceptible to the action of reagents, and, if time be allowed, 
finally become " gummed," and completely altered into resins 
of various degrees of solidity. Such changes are so plainly 
observable, however, that no special tests are necessary to in- 
dicate their commencement or their progress. The mineral 
oils are not subject to such alterations to any serious extent, 
unless very long exposed to the action of oxygen and of light, 
in which case the absorption of the gas and its conversion into 
ozone, with some loss of lubricating power and greater reduc- 
tion of its value as an illuminant, become matters of some im- 
portance. 

97. The Action of Oils on Metals is sometimes important. 
Copper and lead, and other soluble metals, are sometimes found 
in oils; and Dr. Stevenson McAdam found that the second of 
the two metals above named may go into solution to such an 
extent as to injure the quality of the oil as an illuminant very 
seriously. In such cases the metal is usually absorbed by the 
oil from the metallic walls of the vessels in which it is stored. 



l8o FRICTION AND LOST WORK. 

Dr. McAdam found this to occur to such an extent as to clog; 
up the wick and ultimately diminish its capillary attraction so 
much that the light was extinguished. The wicks when 
charred left a fine net-work of lead. The action of the oil on 
tin, copper, and iron was slight, and its illuminating properties 
were not much diminished. Zinc, however, was quickly at- 
tacked, and the oil was as seriously affected as by lead. While 
the vessels for the retention of paraffine-oil may be safely con- 
structed of or be lined with tin, copper, or iron, it would 
evidently be preferable to use tanks lined with enamel for 
storing the oil. 

Detection of Copper and Lead. — To detect the presence of 
copper, mix a small portion of the oil with twice its weight of 
nitric acid in a test-tube, and shake well ; then, separating the 
acid from the oil, add ammonia to the former: if copper is 
present, the reaction will give a blue color by the formation of 
an ammoniacal solution of that metal. 

To detect lead, add to a portion of the oil, contained in a 
test-tube, a small quantity of sulphuric acid, of carbonate of 
soda, or of caustic soda : if lead is present the solution will be- 
come white, and will yield a precipitate of similar color. To in- 
sure certainty, add to the solution caustic soda until the acid,, 
if used, is neutralized, or add acid, if soda has been used, and 
a few drops of sulphur-solution, the presence of lead will be in- 
dicated by a dark-brown precipitate. With bichromate of potas- 
sium or the iodide of potassium, a yellow precipitate is found. 

Dr. Watson concludes,* in regard to this action — 

(i) That of the oils used, viz., linseed, olive, colza, almond,, 
seal, sperm, castor, neat's-foot, sesame, and paraffine, the samples 
of paraffine and castor oils had the least action, and that sperm 
and seal oils were next in order of inaction. 

(2) That the appearances of the paraffine and the copper 
were not changed after JJ days' exposure. 

(3) That different oils produce compounds with copper vary- 
ing in color, or in depth of color, and consequently rendering 



* Paper read in the Chemical Section of the British Association, Plymouth 
Meeting, 1879. 



INSPECTION AND TEST OF LUBRICANTS. l8l 

comparative determinations of their action on that metal from 
mere observations of their appearances impossible. 

He later * experimented further, with the following results, 
noted, after one day's exposure, with iron : 

(i) Neafs-foot. — Considerable brown irregular deposit on 
metal. The oil slightly more brown than when first exposed. 

(2) Colza. — A slight brown substance suspended in the oil, 
which is now of a reddish-brown color. A few irregular 
markings on the metal. 

(3) Sperm. — A slight brown deposit, with irregular mark- 
ings on the metal. Oil of a dark-brown color. 

(4) Lard. — Reddish brown, with slight brown deposit on 
metal. 

(5) Olive. — Clear and bleached by exposure to the light 
and air. The appearance of metal same as when first im- 
mersed. 

(6) Seal. — A few irregular markings on metal. The oil 
free from deposit, but of a bright clear red color. 

(7) Linseed. — Bright deep yellow. No deposit or marks on 
metal. 

(8) Almond. — Metal bright. Oil bleached and free from 
deposit. 

(9) Castor. — Oil considerably more colored (brown) than 
when first exposed. Metal bright. 

(10) Paraffine. — Oil bright yellow, and contains a little 
brown deposit. The upper surface of the metal on being 
removed is found to have a resinous deposit on it. 

The tendency of an oil to act on metals varies with the 
proportion of free acid and kind of oil, and also with the 
nature of the metal. Nearly all fatty oils act more rapidly on 
copper than on iron. The following table shows results ob- 
tained by Watson with iron exposed to the action of oils for 
twenty-four hours and with copper after ten days' exposure : 

* Swansea Meeting, British Association, 1880. 



182 



FRICTION AND LOST WORK. 
ACTION OF OILS ON METALS. 



Oils. 


Iron dissolved 
in 24 days. 


Copper dissolved 
in 10 days. 


Almond 


.0040 grain. 
.0048 
.0800 " 
.0250 " 
.0050 " 
.0875 " 
.0062 " 
.0045 " 
.0050 " 
. 0460 • ' 


. 1030 grain. 


Castor 


Colza 


.0170 grain. 


Lard 


Linseed 


.3000 grain. 
.1100 " 
.2200 " 
,0015 " 
.0485 " 
.0030 " 


Neat's-foot , 


Olive 


Paraffine 


Seal 


Sperm 





There is evidently no relation between the action of an oil 
on copper and the action of the same oil on iron : in several 
instances, those oils which act largely on iron act slightly on 
copper, while those which act largely on copper act little on 
iron. The total amount of action of the same oil (with the 
exception of paraffine and probably other mineral oils) is greater 
on copper than on iron. 

98. Impurities in Mineral Oils consist, usually, of the 
gritty and earthy substances which rise in the well with the 
oil, and of the " still-bottom" impurities which are produced in 
the process of refining. The presence of the latter in other 
oils is the best possible evidence of the admixture of the min- 
eral oils. They may be detected by dropping a little of the 
suspected oil on white blotting-paper, which absorbs the oil, 
leaving the impurities visible as black specks on its surface. 
The abnormally low temperature at which the oil vaporizes in 
contact with these particles is also a means of detecting their 
presence. The presence of mineral oils in other oils may 
sometimes be readily detected by holding a bottle of the oil to 
be examined up to the light, and shaking it well, when the 
appearance of fluorescence in the bubbles of air so formed is 
an unmistakable sign of the presence of petroleum. 

The following method of estimating the proportions of 
mineral and other oils in the common mixtures is given by 
Mr. C. C. Hall,* as based on a method suggested by Sir Wil- 
liam Thomson and Mr. A. H. Allen. 

* Trans. Am. Inst. Mining Engineers, 1882. 



INSPECTION AND TEST OF LUBRICANTS. 1 83 

Four to five grains of the oil under examination are weighed 
out into a porcelain capsule of 75 c.c. capacity. Thirty c.c. of 
a ten-per-cent solution of potassium-hydrate are added, and 
the capsule, covered with a watch-glass, is placed in a water- 
bath heated to about 93 C. The mixture of oil and alkali 
should be stirred frequently, and after three quarters of an 
hour it is boiled with stirring, to secure complete saponifica- 
tion of all vegetable or animal oil. After boiling some time, 
a thick scum of soap forms on the surface ; a little bicarbonate 
of soda is then added to convert the excess of caustic alkali 
into carbonate. When the contents of the capsule have be- 
come pasty, an equal bulk of fine clean sand is stirred in, 
which makes the soap granular, and facilitates the removal of 
the last traces of alcohol. The capsule is heated for two hours 
more on the water-bath. After cooling, the contents are trans- 
ferred to a short-necked funnel, having a thin plug of asbes- 
tos, and washed with petroleum-ether, or other light petro- 
leum-spirit. The ether dissolves out the mineral oil from the 
soap, and is collected in a quarter-litre flask having a short 
neck. Care must be taken to effect a complete removal of the 
oil. This can be tested by letting a drop of the ether, as it 
comes through, fall on a piece of tissue-paper. If no greasy 
stain is left after the ether evaporates, the solution may be 
considered complete. 

Most of the ether is removed from the oil by distillation, 
and can be saved. The heat of the water-bath is sufficient to 
boil it, and the fumes may be condensed by passing them into 
a condenser. The oil is now transferred to a weighed 50-c.c. 
flask, which has a hole blown in its side ; and dry, warm air is 
forced into the flask through its neck in order to remove the 
last traces of the ether. The flask should not be heated above 
the point where it can be borne in the hand : if this precaution 
is heeded, there is no danger that any of the oil will be volati- 
lized. The passage of the air should be continued until the 
flask and oil are constant in weight. 

Sperm-oil cannot be separated from mineral oil by this 
method, owing to the impossibility of completely saponify- 
ing it. 



1 84 



FRICTION AND LOST WORK, 



To determine the proportion of earthy matter in the 
gummy masses sometimes found in steam-engines in which 
organic oils and steam carrying dirty water from the boilers 
have come in contact: 

Weigh out any convenient amount of the deposit ; wash 
well with benzine until it ceases losing weight and all oily 
matter is removed ; dry, and weigh again. 

The proportion of mineral matter usually ranges from 85 
to 95 per cent. 

99. The Density of Oil is the first of its physical charac- 
teristics noted by the inspector in the attempt to determine 

its character. It is, perhaps, the 
simplest and easiest method of iden- 
tifying a standard oil, although by 
no means a certain one. This may 
be done by carefully weighing an 
exactly measured volume of the lu- 
bricant, and comparing its weight 
with the standard volume of a stand- 
ard substance, or by the use of the 
"densimeter," or oleometer. This 
little instrument, generally known 
as the hydrometer, takes its specific 
name from the application for which 
it has been designed ; as, for example, 
lactometer when used to determine 
the density of milk, and alcoholome- 
ter when used to measure that of al- 
cohol. It consists (Fig. 29) of a glass 
or metal cylinder, usually of an inch 
(2.4 cm.) or less diameter, and sev- 
eral diameters in length, carrying at 
the lower end a bulb loaded with 
shot, or mercury, or other heavy 
substance, and on the upper end a cylindrical stem graduated 
in such a manner as may be best suited to the work for which 
it is intended. A cylindrical tank or jar, with attached ther- 
mometer, is nearly filled with the liquid to be examined. 




Fig. 29.- 



-Oleometer and 
Jar. 



INSPECTION AND TEST OF LUBRICANTS. 1 85 

Placing the instrument in the liquid, it floats upright, with 
the loaded end downward, and sinks to such a depth that the 
figure on the stem reads the density or the specific gravity 
(the terms are not precisely synonymous) of the liquid. 

The liquid must usually be tested at standard temperature, 
— say, 6o° F. (15 C), — as its density is considerably affected 
by heat or cold. The hydrometer has a thermometer attached 
to the lower end. This is intended to assist in making cor- 
rections for a temperature above or below 6o°. When 
the thermometer indicates a temperature above 6o°, which is 
shown by the figure on the right side, the corresponding num- 
ber opposite must be added to the indications on the scale 
above. If the thermometer stands below 6o°, the correspond- 
ing number opposite must be deducted. 

100. Specific Gravities and Baume's Scale, often used in 
this work, are not proportional, the latter scale being conven- 
tional. The specific gravity of a substance is proportional to 
its density, and is the ratio of the weight of a given volume of 
the substance to that of an equal volume of water, both being 
usually taken at the temperature of maximum density of the 

latter. For liquids lighter than water, -~ = specific 

53 130+ Baume r 

gravity, and 130 = B°, the reading of Baume. 

sp. gr. 

As illustrating the use of the instrument, assume it to be 
used for obtaining the gravity of an oil — sperm, for example : 
finding it to be 0.8750, or 30 Baume, it would be at once 
concluded to be impure ; because sperm should give about 
0.8810 or 0.8815, corresponding to 29 B. Oils often differ 
considerably in density, although nominally the same. 

The following table gives the specific gravities and Baume's 
''degrees" for liquids heavier than water, as obtained by 
various authorities.* It is evident that the determination 
of the specific gravity, or the use of a carefully standardized 
Baume scale, only can give satisfactory figures. 

* Chandler and Wiechmann. 



1 86 



FRICTION AND LOST WORK. 









BAUME'S 


SCALE AND SPECIFIC 


GRAVITIES. 






a 

CO 

CQ 
v> 
<u 
<u 
u 

i> 
Q 


a* 

^S 


CO 
.a" . 

<u • co 
U TD vo 
3 000 

U 



•a . 


15 "6 . 
° £• 

eg' "? 


en 

c 2" 
H 

°r i 


06 
co 

■"*■ 
§11 




Moo' . 

U Tf 

•S III" 

h" 


co- 
co 

-*■ 

■*■ 

-oil . 

* ° H 

u 


a . 

O m 

a .0° 

<u -a 

Cu 


C/3 4 

£>£°. 

~<A T II 

to ii II 

c~ O 


co 
|» - 

O ° 


d 

.a 

•^ II °3 




>n 
o_ 
<si 




10 


m 


V 0) 


jj- 





m 


u 


m 




V3 "? 


ffi 


X3 • 


in 




N 


H 


£ M 




H 


H 




" 




S !? 


"■ 




u2 


M 


o. . 


1. 0000 


I. OOO 


1. 000 


1. 0000 


1. 0000 


I. OOO 


1. 000 


I. OOO 


1. 0000 


I. OOO 


I. OOOO 


I. OOOO 


I. OOO 


I. OOO 


I.. 


1.0072 


I.OO7 


1.007 


1.0070 


1.0069 


1.008 




1.007 


1.0069 


1.005 


I.0069 


1.0070 


1.007 


1.007 


2.. 


1.0145 


I. OI4 


1. 0142 


1.0141 


1. 0140 


1. 015 




1. 014 


1-0139 


1. on 


I-OI39 


1.0141 


1.014 


1-013 


3-- 


1. 0219 


I.022 


1.022 


1. 0213 


1. 0212 


1.022 




1.022 


1.0211 


1.023 


I.0211 


1. 0213 


1.020 


1.020 


4-- 


1.0294 


I.029 


1.029 


1.0286 


1.0285 


1.029 




1.029 


1.0283 


1.029 


I.0283 


1.0286 


1.028 


1.027 


5-- 


1.0370 


I.O36 


1.036 


1.0360 


1.0358 


1.036 


1.023 


i-°37 


1-0357 


1.036 


I.0356 


1.0360 


1.034 


1-034 


6.. 


1.0448 


I.O44 


1.044 


I -°435 


1-0433 


1.043 




1.045 


1. 0431 


1.043 


1. 043 1 


I-0435 


1. 041 


1.041 


1 ■■ 


1.0526 


I.052 


1.052 


1.0511 


1.0509 


1. 051 




1.052 


1.0507 


1.050 


I.0506 


1.0511 


1.049 


1.048 


8.. 


1.0606 


I.Ofo 


1.060 


1.0588 


1.0586 


1.059 


1.055 


1.060 


1.0583 


1.057 


1.0583 


1.0588 


1057 


1.056 


9-- 


1.0687 


LO67 


1.067 


1.0667 


1.0665 


1.067 




1.067 


1. 0661 


1.064 


1. 0661 


1.0666 


1.064 


1.063 


IO. . 


1.0769 


1.075 


1-075 


1.0746 


1.0744 


1.075 


1.076 


1-075 


1.0740 


1.071 


I.0740 


I-0745 


1.072 


1.070 


ii.. 


1.0853 


1.083 


1.083 


1.0827 


1.0825 


1.083 




1.083 


1.0820 


1.086 


1 0820 


1.0825 


1.080 


1.078 


12. . 


1-0937 


1. 091 


1. 091 


1.0909 


1.0906 


1. 091 


1.090 


1.091 


1.0902 


1.093 


1. 0901 


1.0906 


1.088 


1.085 


13- • 


1. 1023 


1. 100 


1. 100 


1.0992 


1.0989 


1.099 




1. 100 


1.0984 


1. 100 


1 .0983 


1.0988 


1.096 


1.094 


14.. 


I. IIII 


1. 106 


1. 108 


1. nil 


1. 1074 


1. 107 




1. 108 


1. 1068 


1. 107 


1. 1067 


1.1071 


1. 104 


I.IOI 


15 


1. 1200 


1. 116 


1.116 


1.1163 


1.1159 


1.116 


1. 114 


1. 116 


I.H53 


1.114 


I.II52 


i-"55 


1.113 


1. 109 


16.. 


1. 1290 


1. 125 


1. 125 


1. 1250 


1. 1246 


1. 125 




1. 125 


1. 1240 


1. 122 


1-1239 


1. 1240 


1. 121 


1.118 


17.. 


1. 1382 


I-I34 


1-134 


I - I 339 


I-I335 


I-I34 




I-I34 


1.1328 


1.136 


1. 1326 


1. 1326 


1. 130 


1. 126 


18.. 


I-I475 


I.I43 


i-i43 


1. 1429 


1-1424 


i-M3 


1.141 


1. 142 


1.1417 


I-I43 


I.1415 


1.1414 


1,138 


1.134 


19.. 


1. 1570 


1.152 


1. 152 


1. 1520 


1.1516 


1. 152 




1. 152 


1. 1507 


1. 150 


1. 1506 


1-1504 


1. 147 


1.143 


20. . 


1. 1666 


1. 162 


1. 161 


1.1613 


1. 1608 


1. 161 


1. 162 


1. 162 


1. 1600 


1.158 


1. 1598 


1. 1596 


I- 157 


1. 152 


21 . . 


1.1764 


1.171 


1.171 


1. 1707 


1. 1702 


1. 170 


1. 170 


1.171 


1. 1693 


1. 172 


1.169k 


1.1690 


1. 166 


1. 160 


22. . 


1. 1864 


1. 180 


1. 180 


1. 1803 


1.1798 


1. 180 


1. 179 


1. 180 


1. 1788 


1. 179 


1. 1786 


1.1785 


1. 176 


1. 169 


23-- 


1. 1965 


1. 190 


1. 190 


1.1901 


1. 1895 


1. 190 


1. 190 


1. 190 


1. 1885 


1. 186 


1. 1883 


1. 1882 


1. 185 


1. 178 


24.. 


1.2068 


1. 199 


1. 199 


1.2000 


1. 1994 


1.200 


1.200 


1.200 


1-1983 


1. 201 


1.1981 


1.1981 


1. 195 


1. 188 


25- • 


1.2173 


1. 210 


1. 210 


1.2101 


1.2095 


1. 210 


1. 210 


1. 210 


1.2083 


1.208 


I.2080 


1.2082 


I.205 


1-197 


■2.6.. 


1.2280 


1. 221 


1. 221 


1.2203 


1. 2197 


1.220 




1.220 


1. 2184 


1. 216 


1. 2182 


1.2184 


I.2I5 


1.206 


27.. 


1.2389 


1. 231 


1. 231 


1 2308 


1.2301 


1.230 




1. 231 


1.2288 


1. 231 


I.2285 


1.2288 


1.225 


1. 216 


28.. 


1.2499 


1.242 


1.242 


1. 2414 


1.2407 


1. 241 


1. 241 


1. 241 


1-2393 


1.238 


I.2390 


1.2390 


1-235 


1.225 


29.. 


1. 2612 


1.252 


1.252 


1.2522 


1. 2514 


1.252 




1.252 


1.2500 


1.254 


I.2497 


1.2502 


1-245 


1.235 


30.. 


1.2727 


1. 261 


1. 261 


1. 1632 


1.2624 


1.263 


1.260 


1.263 


1.2608 


1.262 


I.2605 


1. 2612 


I.256 


1.245 


3i- • 


1.2844 


1-275 


1-275 


i- 2 743 


1-2735 


1.274 


1-273 


1.274 


1. 2719 


1.269 


1. 2716 


1.2724 


I.267 


1.256 


32.. 


1.2962 


1.286 


1.286 


1.2857 


1.2849 


7.285 


1.284 


1.285 


1.2831 


1.285 


I.2828 


1.2838 


I.278 


1.267 


33- • 


1.3083 


1.298 


1.298 


1-2973 


1.2964 


1.296 


1.296 


1.297 


1.2946 


1.293 


I.2943 


1.2954 


I.289 


1.277 


34- ■ 


1.3207 


1.309 


1.309 


1-3091 


1. 3081 


1.308 


1-307 


1.308 


1.3063 


1.309 


I-3059 


1.3072 


I.3OO 


1.288 


35 •• 


1-3333 


1. 321 


1. 321 


1.3211 


1. 3201 


1.320 


i-3i5 


1.320 


1.3181 


1-317 


1-3*77 


1-3190 


1.312 


1.299 


36.. 


1.3461 


*-334 


1-334 


1-3333 


I -3323 


1-332 


1.329 


1.332 


1.3302 


1-334 


1.3298 


I-33H 


I-324 


1.310 


37 •• 


1-3592 


1.346 


1.346 


1-3458 


I -3447 


1-345 


I -339 


1-345 


1.3*25 


1.342 


1. 3421 


1-3434 


L337 


1. 321 


38.. 


1-3725 


1-359 


1-359 


L3585 


1-3574 


1-358 


1-359 


1-357 


I-355I 


1-359 


I-3546 


1-3559 


1-349 


1-333 


39 •• 


1. 3861 


!-372 


1.372 


L37I4 


1-3703 


i-37i 


L372 


1.370 


1-3679 


1.368 


1-3674 


1.3686 


1.361 


1-345 


40.. 


1-3999 


1.384 


1.384 


1.3846 


1-3834 


1.384 


1-375 


1-383 


1.3809 


1.386 


1.3804 


1-3815 


J-375 


1-357 


41.. 


1. 4141 


1.398 


1.398 


i-398i 


1.3968 


1-397 


1-399 


I -397 


1.3942 


x -395 


1-3937 


1-3947 


1.388 


1.369 


42.. 


1.4285 


1.412 


1.412 


1.4118 


1. 4104 


1. 410 


1-413 


1. 410 


1.4077 


!-4i3 


1.4072 


1.4082 


1. 401 


1.381 


43 •• 


1-4433 


1.426 


1.426 


1.4267 


1.4244 


1.424 


1.427 


1.424 


1. 4215 


1.422 


1. 4210 


1.4219 


1-414 


1-395 


44.. 


1-4583 


1.440 


1.440 


1.4400 


1.4386 


1.438 


1. 441 


1.438 


I-4356 


1. 441 


1-4350 


1-4359 


1.428 


1.407 


45 •• 


1-4735 


1-454 


1-454 


I -4545 


i-453° 


1-453 


i-455 


1 453 


1.4500 


i-45i 


1-4493 


1 4501 


1.442 


1.420 


46.. 


1.4893 


1.470 


1.470 


1.4694 


1 4678 


1.468 


1.466 


1.468 


1.4646 


1.470 


1.4640 


1.4645 


1.456 


1-434 


47.. 


I-5053 


1.485 


1.485 


1.4845 


1.4829 


1.483 


1.482 


1.483 


1-4795 


1.480 


1.4789 


1.4792 


1.470 


1.448 


48.. 


1-5217 


1. 501 


1.501 


1.5000 


1.4983 


1.498 


1.500 


1.498 


1.4949 


1.500 


1. 4941 


1.4942 


1.485 


1.462 


49.. 


1-5384 


1.516 


1.516 


I-5I58 


1. 5140 


I-5I4 


I-5I5 


i-5 x 4 


1. 5104 


1. 510 


I-5097 


1.5096 


1.500 


1.476 


50.. 


1-5555 


^•532 


1.532 


I-53I9 


1. 5301 


i-53° 


i-532 


1 -53o 


1.5263 


I-53 1 


1-5255 


I.5253 


I-5I5 


1.490 


5i- • 


I -5730 


1-549 


1-549 


1.5484 


I-5465 


1.546 


i-55o 


1.540 


L5425 


I-54I 


I-5417 


1-5413 


I-53I 


1-505 


52.. 


1.5909 


1.566 


1.566 


1-5652 


1-5632 


1-563 


1.566 


1.563 


I-559I 


1.562 


I-5583 


I.5576 


1.546 


1.520 


53 • • 


1.6092 


1.583 


1-583 


1.5824 


1.5802 


1.580 


1.586 


1.580 


1.5760 


1-573 


1-5752 


1-5742 


1.562 


i-535 


54- • 


1.6279 


1. 601 


1. 601 


1.6000 


I-5978 


1.598 


1.603 


1-597 


1-5934 


1-594 


1-5925 


1.5912 


1.578 


i-55i 


55 •• 


1. 6471 


1.618 


1. 618 


1. 6179 


1-6157 


1. 616 


1. 618 


1.615 


1.6111 


1. 616 


1.6101 


1.6086 


1.596 


1-567 


56.. 


1.6667 


1.638 


1-637 


1.6363 


1.6340 


1.634 1.639 1 1-634 


1.6292 


1.627 


1.6282 


2.6264 


1.615 


1-583 


57-- 


1.6868 


1.659 


1.656 


1.6551 


1.6527 


I - 6 53 


1.660 


1.652 


1.6477 


1.650 


1.6467 


1.6446 


1.634 


1.600 



P X d 
Note. — Where the modulus was not given, it was calculated by the formula n — — , in which 



» = modulus, P = specific gravity, d = Baume degree (°). 
ing specific gravity appeared. 



66 was taken for d whenever the correspond- 



INSPECTION AND TEST OF LUBRICANTS. 



I8 7 



The next table gives a similar comparison for liquids lighter 
than water with, also, the pounds weight per gallon. In metric 
measure the specific gravity also measures the weight of the 
litre in kilogrammes. 



SPECIFIC GRAVITIES AND DENSITIES, PER BAUME. 



Density 




Lbs. in one 
Gallon. 


Di 


:nsity. 


Lbs. in one 
Gallon. 


B. 


S. G. 




B. 


S. G. 




IO I 


0000 


8-33 


44 


.8045 


6.70 


II 


9929 


8.27 


45 


.8000 


6.65 


12 


9859 


8.21 


46 


•7954 


6.63 


13 


9790 


8.16 


47 


.7909 


6-59 


14 


9722 


8.IO 


48 


.7865 


6.55 


15 


9655 


8.00 


49 


.7821 


6.52 


16 


9589 


7-99 


SO 


•7777 


6.48 


17 


9523 


7-93 


51 


•7734 


6-45 


18 


9459 


7.88 


52 


.7692 


6.41 


19 


9395 


7.83 


53 


.7650 


6.37 


20 


9333 


7.78 


54 


.7608 


6-34 


21 


9271 


7.72 


55 


.7567 


6.31 


22 


9210 


7.67 


56 


.7526 


6.27 


23 


9150 


7.62 


57 


.7486 


6.24 


24 


9090 


7-57 


58 


.7446 


6.21 


25 


9032 


7-53 


59 


.7407 


6.18 


26 


8974 


7.48 


60 


.7368 


6.15 


27 


8917 


7-43 


61 


.7329 


6.12 


28 


8860 


7-38 


62 


.7290 


6.09 


29 


8805 


7-34 


63 


•7253 


6.05 


30 


8750 


7.29 


64 


.7216 


6.02 


31 


8695 


7.24 


65 


.7179 


5.99 


32 


8641 


7.20 


66 


.7142 


5-95 


33 


8588 


7.15 


67 


.7106 


5-92 


34 


8536 


7. 11 


68 


.7070 


5-89 


35 


8484 


7.07 


69 


.7035 


5-86 


36 


8433 


7.03 


70 


.7000 


5.83 


37 


8383 


6.98 


75 


.6S29 


5-70 


38 


8333 


6.94 


80 


.6666 


5-55 


39 


8284 


6.90 


: 85 


.6511 


5.42 


40 


8235 


6.86 


90 


.6363 


5.30 


4i 


8187 


6.82 


95 


.6222 


5.18 


42 


8i39 


6.78 


100 


.6087 


5.01 


43 


8092 


6.74 









101. Densities of Commercial Oils are often determined 
by the more accurate method of determining specific gravity 
by weighing on the chemist's balance. A standard tempera- 
ture is usually adopted, and all results reduced to stand- 
ard by first determining the coefficient of expansion, which 
for pure olive-oil has been determined by Mr. C. M. Still- 



188 FRICTION AND LOST WORK. 

well to be 0.00063 for i° Centigrade, or 0.00035 per degree 
Fahrenheit. 

Mr. Stillwell's determinations are given in the following 
table : 

SPECIFIC GRAVITY OF ANIMAL AND VEGETABLE OILS. 

15 C 

Coeff. of Exp. = .00063 FOR l0 C. 50° F. 

= .00035 for i° F. _____ 

Sperm, bleached, winter 8813 

" natural, winter 8815 

Elaine 901 1 

Red, saponified 9016 

Palm 9046 

Tallow 9137 

Neat's-foot , 9142 

Rape-seed, white, winter 9144 

Olive, light greenish yellow 9144 

Olive, dark green 9145 

Pea-nut 9154 

Olive, virgin, very light yellow 9163 

Rape-seed, dark yellow 9168 

Olive, virgin, dark clear yellow 9169 

Lard, winter 9175 

Sea-elephant , 9 X 99 

Tanners' (cod) 9205 

Cotton-seed, raw. 9224 

Cotton-seed, refined, yellow .9230 

Salad (cotton-seed) 9231 

Labrador (cod) 9237 

Poppy ,. 9245 

Seal, natural . , 9246 

Cocoa-nut 9250 

Whale, natural, winter 9254 

Whale, bleached, winter 9258 

Cod-liver, pure .9270 

Seal, racked 9286 

Cotton-seed, white, winter 9288 

Straits (cod) 9290 

Menhaden, dark 9292 

Linseed, raw 9299 

Bank (cod) 9320 

Menhaden, light 9325 

Porgy 9332 

Linseed, boiled 9411 

Castor, pure cold-pressed. 9667 

Rosin, third run 9887 



INSPECTION AND TEST OF LUBRICANTS. 1 89 

The mineral oils are usually lighter than those of animal or 
vegetable origin. 

The following are the densities of some of the compounds 
found in petroleums: 

Mineral Oils, 6o° F., 15 C. 

S. G. B. 

Rhigoline 6220 95 

Benzine 6510 85 

Naphtha 7000 70 

7500 57 

Illuminating Oil 8000 45 

Lubricating Oil (heaviest) 8860 26 

ParafBne Wax 8900 27 

The " sperm"-oils of the market vary considerably in den- 
sity, partly in consequence of natural differences due to differ- 
ences in age, size, health, and condition of the sperm-whale 
which may have supplied all or part of the oil, and partly be- 
cause of variations in the character and extent of the adultera- 
tion. Professor Ordway found " spindle-oils" to vary in den- 
sity from 0.840 to 0.92, averaging 0.880. Ten so-called sperm- 
oils varied from 0.880 to 0.896, averaging 0.884. Oils from 
newly arrived cargoes ranged from 0.877 to 0.888. Lard-oils 
average 0.917, ranging from 0.914 to 0.920. Neat's-foot oil 
gives an average of 0.912, ranging from 0.910 to 0.920 for a 
sample known to be pure. The addition of refined, odorless, 
heavy mineral oils to other lubricants is a usual cause of in- 
crease of density ; this is particularly the case with lard-oil. 
The common method of making these determinations is by 
the use of the " 1000-grain bottle," or other such apparatus. 

In using the various areometers as oleometers, large jars and 
densimeters having slender, finely graduated stems should be 
employed, their scales reading to 0.001. This can be done by 
constructing the instrument as an oleometer purely, thus being 
able to distribute a small range of density over an extended 
scale. Special oleometers are sometimes made for the mineral 
oils, and others for the organic oils. 

102. The Viscosity of Oil is generally closely related to 
its density, but is not proportional to specific gravity, and is 



190 



FRICTION AND LOST WORK. 



occasionally found to decrease with increase of density. The 
relative viscosity of oils may be determined with some degree 
of accuracy by simply filling a pipette with the oils to be com- 
pared, one after another, and 
permitting them to flow out 
through a small opening, noting 
the time required to discharge 
equal quantities. A very com- 
plete apparatus for this pur- 
pose is that exhibited in Fig. 30, 
a form adopted by Mr. J. V. 
Wilson. 

In the figure, A is a glass 
tube about 1 in. diameter, grad- 
uated from 1 to 100, to contain 
about 100 cubic centimetres of 
oil. BB is a glass jacket, about 
3 in. diameter, filled with water 
as shown; C a thermometer, in- 
dicating temperature of water 
in jacket ; D a small brass cock 
for withdrawing water from 
jacket ; E a glass flask for generating steam to heat water in 
jacket ; F a glass pipe connecting the steam flask E with jacket 
B, delivering at bottom of jacket ; G is a small cock for per- 
mitting escape of steam in order to regulate quantity sent into 
jacket ; H a spirit-lamp on a stand ; J a glass beaker to contain 
oil, and KK cast-iron stand, with adjustable arms, for carrying 
the apparatus. 

The following table gives the time required, by'each of seve- 
ral oils, to flow through the orifice of the above-described ap- 
paratus, and the temperature observed in the same oils when 
used on a journal 3 in. (7.2 cm.) diameter, making 1500 revolu- 
tions per minute, the average being noted for an hour and a 
half. It is seen that, as a rule, the more viscous the oil the 
more heat developed by friction. The stearine found in tal- 
low-oil may cause the apparent discrepancy noted there. 




Fig. 30. — Viscosity of Oils. 



INSPECTION AND TEST OF LUBRICANTS. 



I 9 I 



VISCOSITY OF OILS. 





S. G. at 
6o° F., 
15° C. 


Rate of Flow. 




Name of Material. 


6o° F., 
15° C. 


120 F., 
49° C. 


180 F., 
82° C. 


Developed 
by Test. 


Water 


IOOO 

960 
99O 








Fahr. 


Cen. 


Castor Oil 




132 


41 


158 
155 


70 
68 


Rosin Oil 




Solid 

143 

112 

108 
96 
92 

47 
45 
30 


41 

37 
40 

4i 

33 
37 
30 


26 

25 
29 
30 
28 
28 
25 




Tallow or Animal Oil 




141 


61' 


Neat's-foot Oil 






Rape Oil 


916 
916 

915 

880 

905 
875 


148 
146 
143 
133 
121 
117 


64 
63 
62 


Lard Oil 


Olive Oil 




56 
49 

47 


Mineral Oil 















It is sometimes customary to make the viscosity of oils a 
standard test of quality. In such cases it is usual to compare 
the oils so tested with some well-known oil, as rapeseed, as a 
standard of value. In these cases the size of the containing 
vessel, of the nozzle and its orifice, the head producing flow, 
the material of which they are made, the temperature, and 
other conditions should be carefully specified and made as 
nearly constant as possible. The specific gravity of the oil 
should be ascertained and stated. 

It has been proposed to adopt a standard " viscosimeter" * 
of dimensions as follows: 

A glass cylinder, 22 in. (55.9 cm.) long, 1 \ in. (3.18 cm.) 
diameter, has a brass lower head •§• in. (0.318 cm.) thick. An 
orifice is bored in the centre -^ in. (0.794 cm.) in diameter, 
with bevelled edges chamfered back -J- in. (1.27 cm.), thus pro- 
ducing a sharp-edged orifice. A line marking the 18-in. (45.72 
cm.) level is cut with several finer lines above and below, •§• in. 
(0.318 cm.) apart, ranging from 16 to 21 in. (40.64 to 53.34 cm.) 
above the orifice. The standard temperature is usually 6o° F. 
(15. 5° C). A total flow of as nearly 100 c.c. (6.103 cu - m ls 
secured by adjusting the supply so that the head shall be as 
nearly as possible equal to 18 in. (45.72 cm.) of water, deter- 



* Chemical News, 1884. W. P. Mason. 



192 FRICTION AND LOST WORK. 

mining this head by calculation from the specific gravity of 
the oil. 

Note the time required to discharge the 100 c.c. (6.103 cu - 
in.), and divide this time by that required where water under 
a head of 18 in. (45.72 cm.) is used. This ratio is the measure 
of the viscosity. 

Large consumers of oil sometimes purchase on the basis of 
this kind of test solely. It is regarded as quite as satisfactory 
and reliable as any single physical or chemical test known, and 
as second only to the best testing-machine methods. 

The less the viscosity, consistently with the use of the oil 
under the maximum pressures to be anticipated, the less is, 
usually, the friction. The best lubricant, as a rule, is that hav- 
ing least viscosity combined with greatest adhesiveness. Vege- 
table oils are more viscous than animal, and animal more so 
than mineral oils. The fluidity of an oil is thus to a large ex- 
tent a measure of its value. 

The close relation between the viscosity and the friction- 
reducing power of the oils is well shown in Fig. 31, which 
graphically exhibits this relation as determined by Mr. C. N. 
Waite."* The curves show the relation between the viscosity 
and lubricating power of lard and of light paraffine oil ; the full 
lines represent the readings on the machine, at different tem- 
peratures, multiplied by a constant, and the dotted lines the 
viscosity of the oil. The curves are approximately correct. 
The true curves are probably smooth, and their form mathe- 
matically determinable. 

The relation of viscosities of oils at ordinary temperatures 
is not a measure of their relative standing in this respect at 
higher temperatures, as in steam-cylinders. Oils of great vis- 
cosity at low temperatures are often very limpid when heated. 
Tallow and castor oils are more viscous than sperm when cool, 
but they become very much more fluid when heated, as in 
steam-cylinders. 

103. Gumming, or Drying, is a method of alteration of 
oils usually caused, as already stated, by the absorption of oxy- 

* Proceedings N. E. Cotton Manufacturers' Association, No. 28, 1880. 



INSPECTION AND TEST OF LUBRICANTS. 



*93 



gen and the gradual conversion of the oil into resin. It goes 
on rapidly with the " drying '-oils, slowly with the fixed ani- 
mal and vegetable oils, and is not observed in any important 



RESISTANCE 
240 



230 
220 
210 
200 
190 
180 
170 
160 
150 
140 
130 
120 

no 

100 
90 
80 

70 
60 
50 

40 



\ 
























\ 
























A 
























\ 


\ 
























\\ 
























\ 


\ 

\ 
























\ \ 

\\ 
























\ \ 


\ 
























w 
























\ 


\ 
























\\ 


^ 














V 










\ 














\ 












\ 












\ 


\ 












\ 


b 










\ 












V, 














\ 


h 
























x? 
^ 














^K 


N 










"^ 


^ 












^ 














^ 


^ 
























^ 


-^ ~"-~ 









c0 : 



ro 3 



120 



70° 80° 90° 100° 

Fig. 31.— Viscosity and Lubrication. 
degree in the mineral oils. This gradual increase of viscosity 
and tendency to final conversion into the solid form is one of 
the phenomena noted by the inspector in his examination of 



194 FRICTION AND LOST WORK. 

lubricants. The methods of determination of the character 
of the lubricant in this respect, as practised by various observ- 
ers, differ greatly. The most satisfactory method is probably 
that in which the lubricant-testing machine is employed : this 
method, as conducted by the Author, is simply to test the oil 
as received ; then to expose the journal, still wet with oil, to 
the action of the air, but keeping it protected from dust, one 
day or more, according to the kind of oil, and then to again 
test its friction-reducing power. This process will be fully 
described later (Arts. 132, 136). 

104. Nasmyth's Apparatus for observing the viscosity and 
gumming of oils is very simple. The observer places a drop 
at the top of an inclined plane, and notes the time required 
for it to run down the plane. Of oils which do not gum, the 
least viscous reach the bottom first. Drying and gumming 
oils are retarded in proportion to the rate of drying or of gum- 
ming. Nasmyth used a plate of iron 4 inches wide by 6 feet 
long, on the upper surface of which six equal-sized grooves are 
planed. This plate is placed in an inclined position — say, 1 
inch in 6 feet. 

The mode of testing is as follows : Assume that six varie- 
ties of oil are to be tested, to determine which of them will 
for the longest time retain its fluidity when in contact with 
iron and exposed to the action of air; pour out simultaneously, 
at the upper end of each inclined groove, an equal quantity of 
each of the oils under examination. This is very conveniently 
done by the use of a row of small brass tubes. The six oils 
then make a fair and even start on the race down-hill : some 
are ahead the first day, and others are still ahead the second 
and third day ; but on the fourth or fifth day the bad oils be- 
gin to fall behind by gradual coagulation, while the good oil 
holds on its course : at the end of eight or ten days there is no 
doubt left as to which is the best. Linseed-oil, which makes 
capital progress the first day, is, in the case given, set fast af- 
ter having travelled 18 inches, while second-quality sperm over- 
reaches first-quality sperm by 14 inches in nine days, having 
traversed in that time 5 feet 8 inches. The following table 
shows the state of the oils after a nine days' run : 






INSPECTION AND TEST OF LUBRICANTS. 
VISCOSITY OF OILS.* 



195 



Description of Oil. 



Best Sperm Oil 

Common Sperm Oil.. 

Gallipoli Oil 

Lard Oil 

Rape Oil 

Linseed Oil 



First 
Day. 



ft. in. 

1 lis' 

o 10V4 

10J4 

1 2^ 

1 sVz 



Second 
Day. 



Third Fourth 
Day. Day. 



ft. in. I ft. in. 

4 M 4 6 

4 6 U 4 11 

1 6 1 ey 2 

10%! o 10% 

1 7 I MM 
1 6%\ 1 634 



Fifth 
Day. 



6 



Sixth 
Day. 



ft. in. 

4 6 

5 4 

1 m 

stat. 

1 lY4 

1 6J4 



Sev'th 
Day. 



ft. in. 

4 6y 3 

5 6% 
1 9 



7*4 

^4 



Eighth 
Day. 



ft. in. 

stat. 
5 7% 
1 9H 



1 7% 
stat. 



Ninth 
Day. 



ft. in. 



5 8 



9Y2 



This process is used by the Author. He adopts a surface 
of glass, however, instead of metal. 

A modified apparatus is described by Mr. W. H. Bailey, 
and is illustrated in Fig. 32. It consists of a piece of plate- 
glass set with considerable inclination, and heated, by means 
of a vessel of boiling water, to about 200 F. (93 C), and held 
at a uniform temperature, as indicated by the thermometer at- 
tached. A drop of oil placed at the top will flow down a few 




Fig. 32. — Bailey's Apparatus. 

inches, as in Napier's test, and if permitted to remain upon the 
glass some days will give evidence of any existing tendency to 
gum. A scale on the side of the box affords a convenient 
means of measuring the track of the flowing drop. Watch-oil 
is tested in Switzerland somewhat similarly. If the oil is found 



*Appleton's Dictionary of Mechanics, vol. ii. 



196 FRICTION AND LOST WORK. 

to become decidedly resinous after two or three days' expo- 
sure to heat, it is condemned. 

A very simple and commonly used test of the fluidity of 
the oil consists in dipping into it a piece of blotting-paper, and 
watching the falling drops as it is held above the surface of 
the oil. Should the oil fall in distinct, symmetrical, pearl-like 
drops, it is an evidence of fluidity ; a tendency to spread is the 
indication of viscidity. Retaining the oil on the paper at a 
temperature of 200 F. for some hours, or at ordinary temper- 
ature for some days, will enable the observer to judge of the 
rate of gumming. 

Oil may also be tested by being kept warmed, nearly to the 
boiling-point, in a watch-glass : if it gums in the course of two 
or three days it should be condemned. 

105. The Effect of Heat, and of variation of tempera- 
ture, is very observable with all the fats and oils. Their clas- 
sification into oils, fats, greases, butters, and fatty waxes is 
based upon the assumption that they are observed at ordi- 
nary temperatures. An increase of temperature converts the 
greases and the waxes into oils, and the reverse change solidi- 
fies the oils, converting them into greases, or even into hard, 
waxy solids. Variation of temperature affects every lubricant 
in an important degree, also, in other respects. It changes 
the friction-reducing power, as well as the fluidity of the un- 
guent, and is thus one of the elements necessarily considered 
in determining the value of the lubricant. For out-of-door 
work, unguents must be selected that will " feed " at any tem- 
perature to which they are to be exposed in the working of 
the bearing to which they are supplied ; it is not advisable, 
therefore, to use the same lubricant in winter as in summer. 
Steam-cylinders are best lubricated with mineral oils of heavy 
body and high " fire-test," which test is resorted to with all 
mineral and often with other oils. 

The effect of heat upon the viscosity of oils gives a good 
illustration of the sensitiveness of the oils to changes of tem- 
perature ; and when it is known that the viscosity and the lu- 
bricating power of any oil are usually very closely related, it is 
seen that change of temperature has an exceedingly important 



INSPECTION AND TEST OF IUBRICANTS. 



I 9 7 



effect upon lubricating oils and greases. Fig. 33 exhibits the 
relation of viscosity to temperature in the cases of a number 
of well-known oils. The " spindle-oils" are mineral oils. 



































& 






























1 



































! 




CM 

O 






























f 

1! 




CM 

O 






























i 






O 






























X 






CM 
O 






























i 
\ 






CN 
































1 




a 




























1 


11 






6 




























I'll 


1 

1 , 

1 



































1 


1 

ll 

1 if 




a 




























/l 

/ 1 ! 
i 


J 

































1 < 


\ 

is 

b 































i 


M 


1 1 
1 • 































& 


/ / 

// 


% 


8 




o 






















/ 


/ / 




' 






5 




















X 




/ 




i 






b 


























I 


1 






ON 
















<- 


^x 






y 


w 

/ 








CD 










.--' 




^0"" 








// 












O 



At 6o° F. (15 C.) the viscosity of sperm being 1.00, neat's- 
foot is 3.20; lard, 2.30; olive, 2.18; paraffine 25 grav., 1.23; 
parafflne 29 grav., 1.06. As the temperature rises the viscos- 
ity decreases, neat's-foot being most and sperm least affected 



! 



198 



FRICTION AND LOST WORK. 



by variations in temperature. While at 6o° F. sperm is 20 per 
cent, thinner than the heavy paraffine, yet at ioo° F. (38 C.) it 
is 10 per cent, thicker, the viscosity of the paraffine having 
diminished so much more rapidly than that of sperm. At 
250 F. (121 C.) the oils are all of nearly equal viscosity. The 
effect of heat on the lubricating value of the oils will be ex- 
hibited later. 

It is in consequence of this sensitiveness to heat that the 
testing-machine used by the Author, and described later, has 




Fig 34. 

often been fitted with Hirn's "water-brasses" for the purpose 
of keeping temperature constant when comparing lubricants. 

106. The " Fire-test" determines the temperature at which 
the mineral oils discharge vapors by fractional distillation, and 
that at which the other oils decompose and take fire. 

This " fire-test" is usually made with a piece of appa- 
ratus made especially for the purpose. That of Guiseppe 
Tagliabue is shown in Fig. 34. It consists of a little tank in 
which the oil to be tested is poured. This is placed in another 
large cup, and the space between is filled with water, for ordi- 
nary tests. A lamp beneath supplies the heat, and a ther- 
mometer set in the cup with its bulb in the oil shows the tem- 
perature. 

As the oil becomes heated the observer occasionally applies 



INSPECTION AND TEST OF LUBRICANTS. 1 99 

a lighted match or taper to the opening of the cup. After a 
time a flash is seen when the match is applied, and the flame 
disappears as suddenly as it has appeared. This shows that 
vapor has been produced in sufficient quantity to mix with the 
air above the oil and produce an explosive mixture. The 
temperature now observed is called the " flashing-point." At 
some higher temperature, if the cap is moved to one side and 
a match is applied, the oil takes fire and burns. This is the 
so-called " burning-point." It may be many degrees above the 
flashing-point. 

Many different forms of instrument are in use, some of 
which are described by State regulations, which also prescribe 
the method of test. The closed cup, above described, gives 
a lower apparent flashing or burning point. than is obtained 
with an open cup. The electric spark has been used by sev- 
eral physicists for igniting the vapor. The rate of heating 
should be about 20 F. (n° C.) in a quarter of an hour. 

This method of test is most generally adopted in the ex- 
amination of the mineral oils, which oils are liable to ignition 
if not properly distilled, and thus to give rise to dangerous ac- 
cidents. Lubricating oils defective in this respect have some- 
times set fire to factories when used on heating journals. When 
such oils are used, their evaporation often produces a danger- 
ously large quantity of combustible vapor in the adjacent at- 
mosphere, and this, if fired, may cause a serious conflagration. 
Such oils, in burning, exaggerate the dangers and the difficul- 
ties of the situation by their vaporization. A high fire-test 
and minimum evaporation indicates a good, as well as a safe, 
lubricant. 

The loss by evaporation of a mineral oil may be ascertained 
by placing a known weight in a watch-glass, and maintaining 
it at a constant temperature for a definite period, as at 140 F. 
(6o° C.) for twelve hours. Under such conditions the loss may 
be below one per cent., or it may exceed 25 per cent. A good 
mineral oil should never lose 5 per cent. 

Other oils always gain weight by absorption of oxygen 
and by resinification. They are sometimes subjected to the 
fire-test to ascertain whether they have mineral oils mixed with 



200 



FRICTION AND LOST WORK. 



them. The following are figures obtained by the Author with 
the apparatus just described: 

FIRE-TESTS OF OIL. 



Oils. 


Temperatures — Fahr. and Cent. 


Flash. 


Take Fire. 


Burn. 


West Va. Oil 


F. 

245° 

400-425° 

475° 


C. 

118 
219° 
246° 


F. 

290° 

485° 
525° 


C. 

143° 
252° 

274° 


F. 

300 

500-520° 

525° 


C. 

149° 
260° 


Winter Sperm 


Lard 


274° 





The flashing and the burning points and the temperature 
of decomposition can thus be found, and liability to injury by 
heat determined, or safety in the presence of fire. The stand- 
ard animal and vegetable oils and all mineral oils of good 
"body" and density only decompose or vaporize at a tempera- 
ture exceeding that of the steam in ordinary steam-engines, 
and even steam at locomotive pressure. The heavy refined 
mineral oils are best for the latter application. 

Illuminating oils, consisting partly or wholly of petroleums, 
are seldom permitted to be sold when having a fire-test below 
150 F. (66° C); and lubricating oils are often rejected by 
purchasers if falling under 300 F. (149 C), or losing by evapo- 
ration more than 5 per cent, when kept at a temperature of 
140 F. (6o° C.) 12 hours. This latter may be also considered 
a standard method of test. 

A winter test of 250 F. (121 C.) and a summer test of 300 
F. (149 C.) are usual figures. 

107. " Cold-tests" are made, in some cases, to determine 
the behavior of oil and greases at low temperatures, and 
whether they may be used out of doors in cold weather. All 
the animal and vegetable oils solidify with reduction of tem- 
perature, and usually at but moderately low temperature. 
The greases are hardened by cold. The good mineral oils do 
not congeal at any ordinarily low temperatures, the heavier 
oils freezing at 20 F. (— 6°. 6 C.) and the lighter remaining 
liquid at 0° F. (— 18 C). Summer sperm thickens at about 
65 F. (i8° C), freezing at about 50 F. (io° C.) ; winter sperm 



INSPECTION AND TEST OF LUBRICANTS. 



20I 



at about 50 and 35 F. (i°.6 and io°C.) ; and lard-oil begins to 
harden at 40 F. (4°^ C.) solidifying at 25° F. (- 4 G). 

A good test of capacity to resist low temperatures is as 
follows: Fifteen parts of Glauber's salts are put into a small 
glass vessel, a small bottle of the oil to be tested is immersed 
in this; a mixture of five parts of muriatic acid and five parts 
of cold water is placed over the salt. The temperature is re- 
duced slowly, and when very low the behavior of the oil may 
be observed and noted. Ice alone, or a mixture of ice and 
common salt will prove, probably, equally good. 

Tests of several oils, made at the U. S. Navy Yard, Brook- 
lyn, in 1870, gave the following: 



Oils. 

Sperm, Natural. 

Olive 

Tallow 



Thickens. 
C. F. 



Flow Ceases. 
C. F. 



Solid. 
C. F. 



Lard. 



1 
i° 

2I e 

7° 



34 

5o 

30° 

yO° 
44° 



- 3 

- 8 C 

- 4 C 
i6 c 

o c 



26° 

18° 

24° 

6o° 

32° 



Sp. Gr. 

O.761 
0.933 
0.795 
0.993 
0-959 



Good mineral oils do not solidify at the freezing-point of 
water. 

The best method of test is to first freeze and then, warming 
the oil, note its melting-point. 

108. Tests with Acid. — The addition of concentrated sul- 
phuric acid to oils was found by Maumene and by Fehling to 
produce considerable heat, and they were able to distinguish 
them by measuring the resulting increase of temperature. The 
drying-oils heat most, and disengage sulphurous acid. The 
following determinations are given by Chateau : 

ACID TESTS OF OILS. 



Oils. 



Olive 

Poppy... 

Colza 

Almond. . . 
Rape-seed. 
Linseed. . . 
Sesame. . . 
Castor. . . . 
Cod-liver. , 



Increase of Temperature. 



Maumene. 


Fehling-. 


42° C. 


37°-7 C. 


74°- 5 


37°-7 


58° 


37°-7 


53°-5 


40°-3 


57° 


55° 


133° 


74° 


68° 


74° 


47° 


74° 


103 


74° 



202 FRICTION AND LOST WORK. 

Maumene added 10 c.c. of acid to 50 grs. of each oil. Feh- 
ling used but 15 grs. of oil. The acid had a density of 66° B. 
The results are thus not precisely comparable ; but it seems 
evident that this method is either not at all accurate, or was 
not well practised by one or the other of these investigators. 

Coleman describes* similar tests, in which he added sul- 
phuric acid to rape and to olive oil, and observed a rise of ioo° 
and 68° F. (37°-7 and 20 C.) respectively. The same experi- 
menter saturated cotton-waste with oil and raised its tempera- 
ture to 150 or 200 F. (65°.5 or 93 C.) in an air-bath, noting 
the time required to produce spontaneous ignition and com- 
bustion. Boiled linseed-oil took fire in ij hours, raw oil in 
4 hours, while refined rape-seed oil required 9 hours of expo- 
sure. The addition of 20 per cent, mineral oil greatly retarded 
and 50 per cent, entirely prevented ignition. 

109. Oleography constitutes another, and a very beautiful, 
although rarely practised, method of identifying oils of various 
kinds ; it was introduced many years ago by Professor Tomlin- 
son, who first applied it to the exhibition of the characteristic 
differences between the essential oils, and termed the peculiar 
and beautiful forms thus produced " cohesion-figures." 

It was again brought forward by Dr. Moffat,f and by him 
applied to the identification of the commercial oils and the de- 
tection of adulteration. The process, as perfected by Dr. Mof- 
fat, is now familiar under the name of " oleograph-test." We 
proceed thus : Wash out a large basin very carefully with water 
and alkali until it is chemically free from foreign matter, and 
fill with perfectly clean water. When the surface has become 
quiet, drop upon it a single drop of the oil to be examined. 
The oil at once spreads rapidly over the surface of the water 
in an exceedingly thin film. Presently the film commences 
breaking up, small openings appearing through it, which grad- 
ually enlarge and group themselves into peculiar lace-like pat- 
terns. These lace-patterns continue changing, and finally the 
surface of the water is covered with detached and very minute 



* Trans. Phil. Soc. of Glasgow, 1873. 
f Chemical News, vol. xviii. p. 299. 



INSPECTION AND TEST OF LUBRICANTS. 203 

particles of oil. Each oil, under the same set of standard con- 
ditions, exhibits a peculiar behavior that is always characteris- 
tic of the oil, and which can therefore be made of use in identi- 
fying it. Each oil spreads at a certain rate, and each, at a 
certain instant during the process of change, forms a peculiar 
and characteristic lace. A comparison of the pattern produced 
in testing the several oils and of the times of observation en- 
ables the experimenter to judge, by comparison with his stand- 
ards, whether the oils tested in this way are pure or adulterated. 

In doing this work it is important to be able to secure 
copies of the patterns thus obtained. This is done by a very 
simple and neat process : Provide another basin containing 
water rather strongly colored with ink, and a quantity of white 
blotting-paper cut into pieces of such size and shape that they 
can be laid upon the surface of the water in the testing-basin. 

The observer stands, watch in hand, noting the changes 
progressing in the film of oil. At the proper moment — a half- 
minute, a minute, or two minutes, whichever may have been 
found a proper standard time, measured from the falling of the 
drop — he carefully and quickly lays a piece of his blotting-paper 
down on the film, then as quickly and carefully transfers it 
to the surface of the ink-solution. At the first contact every 
point in the surface transfers to the pages a particle of water 
or a particle of oil, and the lace-pattern is now present on the 
paper in oil and water. On placing the blotting-paper on the 
colored water all parts of the surface unprotected by oil are 
stained, while the rest remains uncolored ; and the beautiful 
lace-pattern appears in black and white in permanent and pre- 
servable form. The sheet is next marked with the name of 
the oil, the date of the test, and the time allowed for the for- 
mation of the pattern. It still remains to be determined by 
further experiment how far the method may be made practi- 
cally valuable and reliable. 

The special precautions to be observed in practising this 
method of test are to secure an absolutely perfect cleanliness 
of the vessels used, and to note with care that oleographic 
figure which is most thoroughly characteristic of the oil under 
test ; this is found to occur at one instant during the uninter- 






204 FRICTION AND LOST WORK. 



rupted process of change of each film of oil, and the patterns 
which precede and which succeed it are comparatively value- 
less. 

The vessels should be cleaned perfectly with a solution of 
caustic potash or soda after each experiment. The oil should 
be let fall in a single drop upon the exact centre of the surface 
of water from a glass rod, and in such a manner that no dis- 
turbance is produced. These rods, when not in use, should be 
kept in a solution of caustic potash, and when used should 
be drawn through clear water and wiped upon a clean cloth 
before dipping them in the oil. 

Occasionally, when the vessels have been some time in use, 
it will be necessary to wash them and the rods in strong sul- 
phuric acid ;* they should then be thoroughly rinsed. 

The symmetry of the figures produced, as well as their 
characteristic form, is injured or destroyed by adulteration, 
and sometimes by physical changes occurring under exposure 
to air, and with age. Solid carbolic acid and camphor treated 
in this manner yield curiously active spots and figures. 

The time at which the distinctive figure is formed is an ab- 
solutely essential element, as already stated ; and it is therefore 
always advisable first to prepare a set of standards by obtain- 
ing the oleographs of oils of known purity. The figures may 
be obtained in any desired color by using colored inks. They 
may be photographed, if desired, or may be transferred to the 
lithographer's stone. 

i io. The Forms of Cohesion-figures are very character- 
istic. In the experiments of Miss Crane, a single drop of oil 
was allowed to fall from a burette held at a distance of a few 
inches from the surface of a dish of clean water. The time 
required for the production of certain figures was carefully 
noted, as several oils will produce very similar figures ulti- 
mately, if sufficient time be given. Oil of turpentine spreads 
out instantly, and soon forms a beautiful lace-work. Oil of 
cinnamon forms a figure not more than half the size of the 
preceding oil. In a few seconds small portions are detached, 

* Chemical News, vol. xiv. p. 64. 



INSPECTION AND TEST OF LUBRICANTS. 205 

and separate into distinct drops. Cod-liver oil spreads into 
a large film ; a little way from the edge small holes appear, 
and in a minute or two the surface is studded with them. 
These gradually enlarge, assume irregular shapes, and become 
separated by branching lines. As the oils give different fig- 
ures, and behave differently when mixed with one another, or 
with lard-oil, this method may be of great value in preliminary 
testing of suspected oils. 

111. Electricity is used in making tests of oil, by noting 
their differences of conductivity. Rousseau has shown that 
the oils, with the exception of olive-oil, which has about yj-g-th 
the conductivity of other oils, are good conductors of electri- 
city, and has devised apparatus to detect adulterations of that 
oil, called the " diagometer." The instruments used are a 
galvanometer and a small voltaic battery, the current from 
which is passed through a drop of the oil to be tested, and its 
intensity measured by the galvanometer. A comparison with 
oils of known purity or of known composition gives the evi- 
dence sought. 

Professor Palmieri has devised a new diagometer, which is 
used for rapid examination of oils and textures. It will show 
the quality of olive-oil ; will distinguish olive-oil from seed-oil ; 
will indicate whether olive-oil, although of the best appearance, 
has been mixed with seed-oil ; will show the quality of seed- 
oils; and will also indicate the presence of cotton in silken or 
woolen textures. 

Mr. F. S. Pease has devised a fire-test igniter, consisting of 
an oil and a water bath, thermometers, an induction-coil and 
battery, and wires for the purpose of testing mineral oils. 
The mineral oils are good conductors of electricity. 

112. Machines for Testing Lubricants are now invari- 
ably used in making determinations of the coefficient of fric- 
tion, and of its variation with varying pressures, temperatures, 
velocities of rubbing, and other conditions affecting the effi- 
ciency of the unguent, as well as in determining its endurance 
and its tendency to gum. These machines consist of a journal 
constructed as nearly as possible like those on which the un- 
guent is to be used, arranged for lubrication in the customary 



206 FRICTION AND LOST WORK. 

manner, or in the way in which the journals to be lubricated 
are " fed," and with apparatus to exhibit the variations of 
speed, temperature, and friction. The aim is always to make 
the test under the actual conditions of practice, as nearly as 
possible. There are a number of forms of these machines, 
some of which will be described in a later chapter, in which 
also the results of experiments conducted upon them will be 
given. 

It is obvious that experiments made upon the nicely fitted 
journal of a testing-machine are not conclusive as to the fit- 
ness of a lubricant for use on a similar journal which is not 
well fitted. The latter bearing only in spots, or along lines of 
contact, is subjected on such surfaces of contact to pressures 
which maybe enormously heavier than that affecting the same 
journal when wear or refitting has given it a good bearing, and 
the best lubricant is therefore one adapted to such intense 
pressure. Could its magnitude be known, a good testing-ma- 
chine would determine which of any collection of oils is best 
fitted for use upon it. The testing-machine determines the 
behavior of an oil upon its own journals; if those on which the 
lubricant is to be used are similar, its behavior will then be 
the same. While the machine does not usually serve to select 
oils for badly made lubricated surfaces, it exhibits the intrinsic 
qualities of the oils tested ; and every mechanic and engineer 
endeavors to get all journals into as good condition as those 
of the testing-machine, and thus fit them to do good work with 
good oils. 

The measure of the coefficient of friction alone is not al- 
ways a gauge of the value of an oil. A low coefficient is some- 
times found to coexist with serious wear ; and even low fric- 
tion and a cool journal may be accompanied by wear. What- 
ever the condition of the journal, however, being reproduced 
in the testing-machine, the position of the lubricant in the 
scale of values may be ascertained. Any difference, whether 
of pressure, speed, temperature, or of form or material of rub- 
bing surfaces, will demand for best effect some corresponding 
difference in the unguent. 

With very light pressures and high speeds, as with fast-run- 



INSPECTION- AND TEST OF LUBRICANTS. 20/ 

ning spindles, light mineral oils sometimes give low friction, 
and yet produce rapid wear. Animal oils in such cases are 
used in solution in the mineral oils to give body and to re- 
duce wear. Heavier machinery, as that of electric-light appa- 
ratus, at high speeds, may be best served with light oils very 
freely supplied, as by the oil-bath, which, indeed, should be 
adopted wherever possible. 



CHAPTER VI. 

EXPERIMENTS ON FRICTION — TESTING-MACHINES. 

113. The Earliest Experiments on the now familiar 
methods of waste of work and energy by friction were made 
at the end of the eighteenth and the beginning of the nine- 
teenth centuries. They were made without regard to the in- 
fluence of what are now known to be essential conditions, and 
were therefore not adequate to determine the facts and laws 
of friction with the exactness and completeness that is desira- 
ble in the engineer's applications in the science and the art of 
construction. 

The best-known experiments of earlier times are those of 
Coulomb on rolling friction, of Rennie on sliding friction of 
unlubricated surfaces, and those of Morin upon the friction 
of solids, both with and without lubrication. 

114. Rolling Friction; Carriages. — Coulomb was the first 
to determine the law of rolling friction, and he found that, so 
long as the wheel or roller and the surface on which it rolled 
were not injured, the resistance was proportional to the weight,. 
and diminished as the diameter of the wheel increased. 

Coulomb and others have, as has been seen, found 

in which R is the resistance applied at the circumference of the 
wheel, Wthe total weight, r the radius of the wheel, and /a 
coefficient which is very variable, but may be taken as 0.06 for 
wood and 0.005 for metal, where the units are lbs. and feet, 
and / = 0.02, nearly, and/ = 0.002 when in metric measures. 
Tredgold makes the value of /for iron on iron 0.002. 



EXPERIMENTS ON FRICTION— TESTING-MACHINES. 20g 

When the pressure becomes so great as to crush the fibres 
of the wood, the friction is increased irregularly, and cannot 
be estimated with any degree of accuracy. 

Experiments similar to those made by Coulomb in 178 1 were 
also made by Morin at the Conservatoire des Arts et Metiers, 
Paris, in which oak-rollers 9 inches (0.26 m.) in diameter were 
used under small loads, and rolling upon poplar rails. Morin 
also found that the resistance increased with diminishing bear- 
ing-surface. 

With a bearing of 0.656 feet, or 9 inches, and loads of 350 
to 450 lbs., the value of / was found to average 0.002874; 
with bearing of a total width of 0.081 feet, or 10 inches, and 
loads of 375 to 450 lbs., the value was f = 0.006374, both 
in British measures, or/"= 0.0009, nearly, and/= 0.002, for 
metric units. The measure of this friction is the moment, Rr, 
which may be called the moment of rolling friction. 

The same laws were, about 1840, found by Morin to be ap- 
plicable to vehicles with little modification. He states that — 

(1) On pavements and macadamized roads the resistance 
is proportional to the total weight of load and vehicle, is in- 
versely proportional to the diameter of wheel, and is independ- 
ent of the breadth of the tire. It increases with the velocity. 

(2) On soft ground the resistance decreases with increase 
of breadth of tire, and is unaffected by the speed of the vehicle. 

(3) The line of draught should be horizontal. 

The conclusions relative to rolling resistance on hard roads 
are also applicable to railroads. 

It follows that wheels should be made as large as possible, 
and the breadth of bearing as great as is needed to prevent 
crushing of the material. Morin found four-wheeled carts to 
be preferable to those having a single pair of wheels.* The 
value of f for wagons was, on soft soil, about 0.065 (0.02 for 
metric measures), but under very favorable conditions became 
as low as f = 0.02 (0.006 metric), which value may be taken 
for the friction of motion on smoothly paved and macadam- 
ized roads. 

* Vide Experiences sur la Tirage des Voitures, etc., A. Morin, 1842. 






2IO FRICTION AND LOST WORK. 



Later experiments upon more modern forms of vehicles 
give results as follows : 

Debauve (1873) found the resistances on macadamized 
roads to vary from 0.033, or 70 lbs. per ton, for heavy carts, 
to 0.036, or 80, for carriages ; and from 0.018 to 0.036, or 40 to 
80, on paved streets, for the same classes of vehicles. 

Tresca found the resistance of an omnibus to be, at ten 
miles an hour, 0.036, 80 to 85 lbs. per ton, on macadamized 
roads, and 0.03, 65 or 70, on paved streets. 

The draught of heavy wagons becomes as high as o. 10 — 
224 lbs. per ton, and usually is not far below 0.07 — about 150 
lbs. per ton on soft ground, as in fields. 

A committee of the Society of Arts reported a loaded om- 
nibus to exhibit a resistance * on various roads as below : 

Pavement. Speed. Resistance. 

On Granite paving 2.87 miles. 0.007 — 17-4* lbs. per ton. 

" Asphalt 3-56 " 0.0121= 27.14 " 

" Wood 3-34 " 0.0185= 41.60 " 

" Macadamized, gravelled 3.45 " 0.0199= 44-4 8 " 

granite, new. . .3.51 " 0.0451 = 101.09 " 

M. Lavallard (1884) found the resistance of omnibuses on 
various pavements and at various speeds to range from 1.5 to 
1.9 per cent, of the total load, or from about 35 to about 45 
lbs. per ton, averaging not far from 1.7 per cent., or 37-J- 
lbs. per ton. The horses used travelled about 16,000 metres 
(10 miles nearly) per day, doing work at the rate of from 
\ to -j- 1 ^ horse-power, as developed by a steam-engine work- 
ing 24 hours continuously. 

Clark deduces from published experiments the formula 



R = 30 -j- 4V -f- V iov. 

in which the resistance, R, is given in pounds per ton, the velo- 
city, v, being taken in miles per hour, and the road being as- 
sumed to be well macadamized. The same authority states 
that a good Flemish draught-horse will work at the rate of 
about 22 ton-miles per day in summer, and 28 in winter, aver- 

* Clark's Manual for Mechanical Engineers, 1877. 



EXPERIMENTS ON FRICTION— TESTING-MACHINES. 211 

aging 25 for the year, this work being the product of load trans- 
ported by distance traversed. 

115. A Railway Train in good order and on a good road 
will not be safe against starting under the action of gravity 
alone unless the gradient is less than 0.0035 — 18 or 20 feet to 
the mile; once started, it will continue in motion on gradients 
as low as 0.0024 — 13 feet per mile. 

Wellington finds the resistance to starting twice or thrice 
the above with ordinary trains on fairly good track, and con- 
cludes that rolling friction forms but a small proportion of the 
total. Trautwine makes the rolling friction about one pound 
per ton, the remainder being journal and flange friction. 

Rolling friction is usually overcome by an effort applied at 
the axis of the wheel or roller, as in cars, wagons, etc., but some- 
times by a force applied at the circumference. In the latter 
case the " moment" or leverage of the applied force is greater, 
and its required intensity correspondingly reduced to one half 
the former. 

Where journals are carried on friction-rollers, the rolling 
friction thus introduced is added to the total resistance ; but 
the sliding-journal friction is reduced nearly in the proportion 
of the diameters of the friction-rollers to the diameters of the 
journals of the latter. The total work of friction, which is the 
product of the resistance into the distance through which that 
resistance is overcome, is thus often greatly reduced. In cases 
in which the frictional resistance is increased there will still be 
an economy of power if the work of friction can be at the same 
time lessened in a greater proportion. 

The resistance on railroads under average conditions, and 
including all forms of resistance, is given by Clark, in pounds 
per ton, as : 

v 2 
For train only, . . R = 6 -] ± 2240/. 

v 2 
For engine and train, R = 3 -] ± 22401. 

h 
Where i = inclination of track = — — . 

5280 



212 FRICTION AND LOST WORK. 

On street railroads the resistances of the cars are greater, 
and sometimes four times as great, as on railroads. Hughes 
found on an English " tramway" a resistance of 0.0115, 26 lbs. 
per ton. 

These frictional resistances are sometimes on railroads 
greatly increased by the resistance of the air, which as " head 
resistance" amounts — in pounds per square foot of front ex- 
posed — to 0.005 of the square of the velocity, in miles per hour, 
with which the air meets the head of the train. Side-winds often 
increase the flange-resistance seriously, and thus greatly add 
to the power required in hauling trains. 

Rankine gives* for the resistance of single railroad-carriages 
having cylindrical wheels, 

in which R is the resistance in pounds, r is the radius of curva- 
ture of the line in miles, and T is the load in tons. 
From Gooch's experiments is derived 

i?=[6 + o. 3 (F- io)j (T+2E); 

and from Harding and Russell, 

\ 3 / v ' J ' 400 

in which last two Vis the speed in miles per hour, E the weight 
of engine in tons, and A is the area of front of train in square 
feet.f 

American trains have on good tracks exhibited much less 
resistance than is estimated as above. 

The following table gives the coefficients of rolling friction ; 

W 
i.e., it gives values of f for the formula R = f — , in which R 

is the resistance, J^the total weight, and r is the radius of the 
wheel or the roller. 

* Exper. Inquiry on the Use of Cylindrical Wheels on Railways, 1842. 
f App. Mec, p. 620. 



EXPERIMENTS ON FRICTION— TESTING-MACHINES, 213 

Value of/ 

Kind of Road. British. Metric. 

Newly-laid sand or gravel 0.067 0.045 

Stony, in ordinary condition 0.05 0.035 

Well-paved 0.02 0.015 

Hard, smooth ground 0.02 0.015 

Well macadamized and rolled 0.015 0.01 

Smooth wooden pavement 0.01 0.007 

Ordinary railroads 0.003 0.002 

Well-laid railroad- track 0.002 0.0015 

Best possible railroad 0.001 0.0007 

The resistance of trains running on curves has been studied 
more recently by Mr. S. Whinery, who deduces for total resist- 
ance the following formula:* 

in which R is the total resistance, D the degrees of curvature, 
^the gauge of the track, / the length of rigid wheel-base, and 
a and n are quantities expressing resistances due to accidental 
and irregular conditions. 

The resistance is inversely as the radius of curvature, directly 
as the load, and nearly independent of the velocity. 

Wellingtonf makes the following comparison of train-resist- 
ances for various methods of lubrication at the speed of ten 
miles per hour for ordinary work : 

Lbs. per ton. 

Tower's experiments, bath of oil 0.278 

pad or siphon 1.9 

Thurston's experiments, light loads 2.75 

heavy loads 1.75 

Wellington's experiments (gravity-tests of cars in service): 

light loads 6.0 

heavy " 3.9 

direct tests (as shown in Fig. 2) \ *" 

<3-7 

Thurston's experiments, inferior oils i 4 " 

I 3-o 
Morin's experiments, continuous lubrication 6.0 to 10.8 

* Trans. Am. Soc. C. E., April, 1878. 
f Trans. An, Soc. C. E., 1884. 



214 FRICTION AND LOST WORK. 

It is concluded that a minimum resistance is reached usually 
at a speed between 10 and 15 miles per hour, but that the in- 
crease is not usually great at higher speeds where the common 
system of lubrication is practised. The Author finds evidence 
that in ordinary work the resistance varies from as low as 4 
lbs. per ton of train up to 25, and even sometimes above 30 lbs., 
per ton. 

Chanute* thus analyzes the increase of resistance at 25 
miles per hour, when the resistance is increased by curvature 
about 0.4 lb. per degree and per ton : 

Due to twist of wheel 0.001 

" slip of wheel 0.1713 

4 ' flange-friction o. 2450 

" loss at couplings 0.0213 



Total 0.4386 

Loose wheels reduce this loss 20 or 25 per cent. The rigid 
form of wheel-base of European cars and locomotives doubles 
the increase due to curves, as well as increases the resistance 
on the straight line. The " coning" of wheels somewhat in- 
creases the resistance — according to Chanute — from o.\2\ to 
0.25 lb. per degree of curve and per ton. 

Professor Franck,f studying the earlier experiments of 
Vuillemin, Guebhard and Dieudonne, and of Rockl, obtains 
the formula for resistance, 

w = m — —fi-t 

in which w is the resistance in kilogrammes per tonne, Q is 
the weight in tonnes, m, /, and F are coefficients, as follows : 

For passenger-engines m = 0.0032 

" freight-engines m = 0.0038 to 0.0039 

" the cars m = 0.0025 

" all cases / =0.1225 

' ' passenger-engines F = 7 

' ' freight-engines F = 8 

' ' passenger and box cars F = o. 5 

' ' unloaded flat cars F = 0.4 

" loaded flat cars F = 1.0 

* Trans. Am. Soc. C. E., April, 1878. 

f Memoirs de la Societe des Ingenieurs Civils, 1883. 



EXPERIMENTS ON FRICTION— TESTING-MACHINES. 2\$ 



He considers that this formula., used with these constants, 
will allow of very exact calculation of the resistance of trains. 

116. Rennie's Experiments on Friction of Solids, usu- 
ally unlubricated and dry, led to the following conclusions:* 

(i) The laws of sliding friction differ with the character of 
the bodies rubbing together. 

(2) The friction of fibrous materials is increased by in- 
creased extent of surface and by time of contact, and is 
diminished by pressure and speed. 

(3) With wood, metal, and stones, within the limit of abra- 
sion, friction varies only with the pressure, and is independent 
of the extent of surface, time of contact, and the velocity. 

(4) The limit of abrasion is determined by the hardness of 
the softer of the two rubbing parts. 

(5) Friction is greatest with soft and least with hard 
materials. 

(6) The friction of lubricated surfaces is determined by the 
nature of the lubricant, rather than by that of the solids 
themselves. 

Experimenting with cloth, Rennie found the resistance to 
starting to vary with time of rest from one third to even more 
than the total weight. Increase of surface-area produced great 
increase in the angle of repose. The following table gives 
values of the coefficient of friction of rest for loads on the 
metals up to the limit of abrasion, as given by Rennie : 



FRICTION OF REST. 



Pressure. 


Values of f. 


Pounds 

on square 

inch 


Kilogramme 

on square 

metre. 


W H 
VV rought- 

iron on 

Wrought-iron. 


Wrought on 
Cast Iron. 


Steel on 
Cast-iron. 


Brass on 
Cast-iron. 


i86f 

224 

336 

448 

560 

672 

784 


131,220 
I57.460 
236,200 
314.932 
393.664 
472,396 
551,128 


O.25 
O.27 
O.31 
O.38 
O.41 
abraded. 


O.28 
O.29 
0.33 
0.37 
0.37 
O.38 
abraded. 


O.30 
0.33 
0.35 
0.35 
O.36 
O.40 
abraded. 


O.23 
0.22 
0.2I 
0.2I 
O.23 
O.23 
O.23 



Philosophical Transactions, 1829, p. 169. 



2l6 FRICTION AND 10 ST WORK. 

After abrasion begins, the coefficient rises as the pressure 
increases. The pressure at which this increase begins to be 
observable is as low as 8 lbs. per square inch (0.6 kg. per sq. 
cm.) with pure tin. 

Rennie, using tool-steel, found it to abrade at a pressure 
of 10 tons per square inch (1575 kgs. per sq. cm.). He re- 
marks that the hardening property of steel, and its great 
power of resisting abrasion, make it superior to all known 
metals for use in delicate instruments, as in pendulums and 
balances, where these properties are essential. 

The same experimenter, among other researches, deter- 
mined the friction of ice upon ice, finding it to vary from I2J- 
per cent, under a pressure of one ounce per square inch (0.0046 
kg. per sq. cm.) down to if per cent, where the pressure rose 
to 9 lbs. per square inch (0.6 kg. per sq. cm.) After six- 
teen hours' contact, the friction was unchanged at the lower 
limit, but became 4 per cent, under the higher pressure. The 
friction of steel skates was 4 per cent, at a pressure of 2 
lbs. per square inch (0.014 kg. per sq. cm.), but only 1^ per 
cent, at 200 lbs. per square inch (14 kgs. per sq. cm.) 

117. Friction of Brakes and Rails. — The most instruc- 
tive experiments upon the friction of unlubricated metals 
under heavy pressures are probably those obtained on rail- 
roads by the use of continuous brakes. The data which are 
perhaps most commonly used in estimating the adhesion of 
engines are those given' in Molesworth's Pocket-Book, which 
are as follows : 

Adhesion per Ton (of 2240 Lbs.) of Load on the Driving-wheels. 

When the rails are very dry 0.268 = 600 lbs. per ton. 

" " wet .. 0.241 = 550 " " 

In ordinary English weather 0.200 = 450 " " 

In misty weather, if the rails are "greasy" 0.134 — 3°° " " 

In frosty or snowy weather 0.089 — 2 °° " " 

If these figures are compared with experiment, it will be 
found that practically a locomotive will, at slow speed and 
under favorable circumstances, pull a heavier load, and that 
at high speeds it will not pull as much as the figures show that 
it should — a consequence of the now ascertained fact that the 



EXPERIMENTS ON FRICTION— TESTING-MACHINES. 217 

resistance is affected by speed, as well as by pressure and by 
temperature. 

A series of experiments were made on the Paris and Lyons 
Railroad " with a wagon, presumably having four wheels, of 
which the brake was screwed up, so that the wheels were 
skidded." The resistance to traction or the friction on the 
rails, at various velocities, is given as follows by Poiree: 

FRICTION OF IRON ON IRON. 







State of the Rails. 




Empty Wagons. 










3.40 tons. 


Dry. 


Very Dry. 


Damp. 


Dry and Rusty. 


Velocity of wagon 


Coefficient of 


Coefficient of 


Coefficient of 


Coefficient of 




Friction. 


Friction. 


Friction. 


Friction. 


Miles per hour. 


Weight = 1. 


Weight = 1. 


Weight = 1. 


Weight = 1. 


9 to 14 


0.208 






0.20I 


14 to 18 


0.179 


O.246 




O.182 


18 to 20 


0.167 




O. I IO 


O.I75 


22 to 23 




0.222 




O.162 


30 to 40 


0.144 


0.202 






40 to 50 




O.187 


O.083 


O.136 



From these experiments it will be seen that the friction 
with a dry rail at a speed of 9 to 14 miles per hour is equal to 
about one fifth of the load, while at 30 to 40 miles per hour it 
is about one eighth.* 

The following table shows the result obtained by Captain 
Galton and Mr. Westinghouse by the sliding of the wheel on 
the rail, that is, steel tires on steel rails:, 



FRICTION OF STEEL ON STEEL. 



Average Speed per Hour. 


Coefficient of Friction: 


Miles. 


Kilometres. 


Commencement of experiment to 3 seconds. 


IO 
15 
25 
38 
45 
50 


17 

25 
42 
60 

75 
80 


O.I TO 
O.087 
0.080 
0.051 
O.047 
O.04O 



* Railroad Gazette, September 20, 1878. 



218 



FRICTION AND LOST WORK. 






From these two tables it will be seen that the results ob- 
tained differ very widely, and that the coefficients given by 
Poiree are almost twice as great as those given by Captain 
Galton. In one respect, however, they agreed, which is that 
the friction diminishes very rapidly as the speed increases.* 

By applying the coefficients given in the preceding tables, 
and calculating the adhesion of locomotive-wheels, we have 
the following table, in which the coefficients given in the 
second column of Poiree's table are employed in making the 
calculation. The coefficient for a speed of 22 to 30 miles per 
hour and for 40 to 50 miles per hour not being given in this 
column, the approximate quantities 0.156 and 0,133 have been 
used in the calculations. 



ADHESION PER TON (2240 LBS.) LOAD ON THE DRIVING-WHEELS. 





Poiree. 


Galton and Westinghouse. 


Speed in miles 
per hour. 


Adhesion. 


Speed in miles 
per hour. 


Adhesion. 


9 to 14 
14 to 18 

18 to 22 
22 tO 30 

30 to 40 
40 to 50 


465.9 lbs. per ton. 
400.9 " " 
374.0 V 

349-4 " 
322.5 " 

297.9 " 


IO 

15 
25 
33 
45 
50 


246.4 lbs. per ton. 
194.8 " 
179-2 " 
127.6 " " 
1 14. 2 " " 
89.6 " 



The results given by Poiree's data at the slow speeds do 
not differ very widely from the data as given by Molesworth. 

The Galton-Westinghouse experiments also show that the 
friction of brake-shoes on the wheels follows the law that 
governs the friction of the wheels on the rails. 

The following table shows the more important results :f 



* Railroad Gazette, September 20, 1878. 
j- London Engineering, August 23, 1878. 



EXPERIMENTS ON FRICTION— TESTING-MACHINES. 2ig 
FRICTION OF BRAKES. 



Average Speed. 



Per second. 



Per hour. 



Coefficient of Friction 
Between Cast-iron Brake-blocks and Steel Tires of Wheels. 



Feet. 
7 
14 
35 
43 
58 
73 



Miles. 
5 
10 
20 
30 
40 
50 
60 



Kilom. 
8 
17 
33 
50 
70 

85 
100 



1st 3 seconds. 


5 to 7 sec. 


O.360 




O.320 


O.209 


O.205 


0.175 


O.184 


O. Ill 


O.134 


O. IOO 


O. IOO 


O.O7O 


O.062 


O.O54 



12 to 16 sec. 



O.I28 
0.098 
O.080 
O.056 
O.048 



24 to 25 sec. 



O.070 



O.O43 



The coefficient with wrought-iron shoes at 18 miles (30 
kilom.) per hour was 0.170, at 31 miles (50 kilom.) 0.129, at 48 
miles (80 kilom.) 0.110; being somewhat less than with cast- 
iron, but the difference is not very marked. 

Captain Galton concludes that " it may be assumed as an 
axiom that for high velocities a brake is of comparatively 
small value unless it can bring to bear a high pressure upon 
the surface of the tire almost instantaneously, and it should be 
so constructed that the pressure can be reduced in proportion 
as the speed of the train is reduced, so as to avoid the sliding 
of the wheels on the rails." * 

His conclusions are thus summarized : 

(1) The application of brakes, when a " skidding" of the 
wheels does not occur, does not seem to reduce their rate of 
rotation. 

(2) Skidding occurs immediately when their velocity is re- 
duced below that due to the speed of the train. 

(3) Resistance is reduced by "skidding" the wheels. 

(4) The pressure required to produce skidding is greater 
than that needed to hold the wheels while skidding. 

(5) The pressure of the brake-blocks must be proportional 
to the coefficient of friction. 

The experiments of the British Commission on Accidents, 
1877, with the continuous brake, gave, as best results, the fol- 
lowing: 



* Railroad Gazette, 1877. 



220 FRICTION AND LOST WORK. 

Weight of engine, tons 35.7 

" " tender, " 14.5 

" " train, " 13,0 

Number of brake-vans 20 

Weight of loaded train, tons 207 .0 

Friction of train, per cent 0.40 (?) 

" " engine and tender, per cent o 60 (?) 

Resistance by brake, per cent 10.6 

Distance, at 60 miles, before stop, feet .1128.0 

Time of applying brake, seconds 1.5 

" " removing " " 3.0 

The length of stop was, approximately, in feet, one ninth 
the square of the speed in miles per hour. The coefficient of 
friction between wheel and brake was less as speed increased, 
varying from about 0.25 at starting to 0.15 at forty miles per 
hour. 

Riveting, in steam-boilers and bridge-work, or other con- 
structions, is usually taken as having a coefficient, f =. 0.333; 
but it should never be reckoned upon as an element of definite 
value, although the enormous pressure produced by the shrink- 
age of heated rivets, while cooling, gives it some importance. 
The elastic limit of common iron is usually not far from 25,000 
lbs. per square inch (1757.5 kgs. per sq. cm.), and one third 
this amount, above 8000 lbs. (562.4 kgs.) per unit of section of 
rivet, is a quantity of real value as an element of safety. 

118. The Friction of Belts and of Gearing has been often 
studied experimentally. Morin concluded its amount for belt- 
ing to be proportional to the angle on the pulley subtended by 
the belt, to the logarithm of the ratio of tensions, and to be 
independent of the width of belt and of the linear measure of 
the arc embraced by it — i.e., independent of the area of con- 
tact. He obtained /= 0.28 to/= 0.38, the value varying with 
the condition of the belt. 

Adopting the formula of Prony for the difference of tension 
on the two parts of the belt, the values of its coefficient, k y 
were obtained as in the table. 

The maximum difference of tension allowable is 

D= T,~ T, = (k-i)T r 



EXPERIMENTS ON FRICTION— TESTING-MACHINES. 221 
The minimum tension allowable to prevent slip is taken as 

VALUE OF k IN PROXY'S FORMULA. 



Proportion of 
Circumference 


New Belt 
on Wooden 

Pulleys. 


Ordinary 
on Wood. 


Belts on 
Iron. 


Wet Belts I 
on Iron. 


Rope on Wooden 
Axles. 


in contact. 


Rough. 


Smooth. 


0.20 


1.9 


1.8 


1-4 


1.6 


1.9 


i-5 


O.40 
O.60 
O.80 


3-5 

6.6 

12.3 


3-3 

5-9 

10.6 


2.0 
2.9 
4.1 


2.6 
4.2 
6.8 


3-5 

6.6 

12.3 


2 3 

3 5 
5 3 


I. OO 


23.1 


19.2 


5-3 


10.9 


23-9 


S.o 


I.50 










in. 3 


22.4 


2.00 
2.50 








- 


535-5 
257.43 


63.2 
173.5 



The maximum stress allowable on the leather was stated at 
about 350 lbs. per square inch of cross-section. 
In the equations'* 



R 



7;= 7; (i -*/•) = r 2 (^-i), 

T y + T 2 ef* + 1 



2R 



2{e' 9 - i) ! 



/"varies from 0.15 to 0.6, the former value being found only 
where the belt is actually wet with oil. 

Reuleaux takes /*= 0.25, and the experiments of Messrs. 
Towne and Briggs-f indicate that this value is exceeded, under 
ordinary working conditions, more than 60 per cent. 

Rubber belting has greater adhesion than leather, and 
values of /"may be used exceeding very greatly those adopted 
for leather. 

The angle 6 = 27m, where n is the number of turns or part 
of turns taken by the belt about the pulley. Rankine givesf 
the following values of the coefficient 2.7288/ in the equation 



* Chapter II., §31. 

f Journal of the Franklin Institute , 1868. 

% Machinery and Mill Work, p. 352. 



222 



FRICTION AND LOST WORK. 



ef* = io 2 -7 28S /« which comes into use in the application of these 
formulas, as seen in Chapter II.: 



/=o.i5 

2.7288/= 0.41 



0.25 
0.68 



0.42 
1. 15 



and, where 6 = n and n = J, as is usual, 



T x 

& + TJ 



T 2 = 1.603 
R = 2.66 
2R — 2.16 



2.18J 
1.84 
1-34 



3758 

1.36 

0.86 



0.56 
i-53 



5.821 
1. 21 
0.71 



Usually we assume T 2 —R; T 1 — 2R\{T 1 -\-T^)-^2R=i.i ) 
and/ becomes 0.22. 

Rankine* gives f for a wire-rope running on cast-iron at 
0.15 and on gutta-percha at 0.25. 

Clarkf gives the following table based on the work of Mr. 
H. R. Towne, and taking the working stress on the belt at 66-f 
lbs. per inch in width for single belts. 

DRIVING POWER OF LEATHER BELTS. 







Horse-power 


Transmitted 




Pressure on 

Journals, 

Pounds 

per 1 inch 

of width. 


Arc of 


Stress on the 

Belt 

per Inch. 


per Inch 


n Width. 


Sum of 
Tensions 
per 1 inch 
of width. 


Contact. 


At 1 ft. per 
Second, 


Per ft. Diam. 
and per Rev. 






Speed of Belt. 


per Minute. 






90° 


32 33 


0.059 


O.OO308 


IOT.OO 


71.42 


IOO° 


34-8o 


O.063 


O.OO331 


9853 


75-47 


IIO° 


37-07 


O.067 


O.OO353 


96.26 


78.85 


120° 


39.18 


O.071 


O.OO373 


94-15 


8i.53 


1 50° 


44.64 


O.081 


O.OO425 


88.69 


85.67 


180 


49.01 


O.089 


O.OO467 


84.32 


84.32 


210° 


52.52 


O.O95 


O.OO500 


80 8l 


7805 


240 


55-33 


O.IOO 


O.OO527 


78.OO 


67.59 


270° 


57.58 


0.105 


O.OO548 


75-75 


53-56 



Rope-gearing has a value of f = 0.25 to f = 0.8, and the 
resistance to slipping is increased in proportion to the cosecant 
of the half-angle of the wedge-shaped groove of the carrying- 
wheel.^: 

* Machinery and Mill Work, p. 352. 

f Manual for Mechanical Engineers, p. 750. 

X American Machinist, November 1, 1884. 



EXPERIMENTS ON FRICTION— TESTING-MACHINES. 223 

In Tests of Gearing, by the Author, the following combina- 
tions were used: (1) An ordinary worm and wheel, the worm 
•double-threaded, 2-inch pitch ; pitch diameter, 6 TU - inches ; 
length of worm, 4^| inches; the wheel of 15-^J inches pitch 
diameter, 2J inches face; velocity-ratio, 25 to 1; worm of 
bronze, wheel of cast-iron. (2) An Albro-Hindley worm and 
wheel, worm 6f inches ; pitch diameter, 5 inches long ; velocity- 
ratio, 25 to 1 ; worm and wheel cast-iron. (3) Two pairs of 
spur-wheels and pinions, the wheels having 80 teeth, "4 pitch," 
and the pinion 16 teeth, giving a final velocity-ratio of 25 to 1. 

The ordinary worm was driven at speeds varying from 41.6 
to 337 revolutions per minute, giving speed of gear of 1.66 to 
13.43 revolutions. The horse-power transmitted to the gear- 
ing ranged from 0.2 to 4.14, and that taken off at the brake 
from 0.55 to 1.77; efficiency, from 0.268 to 0.458. 

The Albro-Hindley worm, under precisely similar circum- 
stances, gave an efficiency ranging from 0.33 to 0.64. In both 
instances a sperm-oil bath was used for lubrication. 

In testing the spur-gearing, the speeds of the driving-pinion 
were from 36 to 231 revolutions, the horse-power communi- 
cated to the train from 0.18 to 2.67; power delivered, from 
O.133 to 2.21 ; efficiency, 0.51 to 0.92. 

The efficiency, in the case of the ordinary worm-gearing, 
increased with the velocity up to 221 feet of rubbing per 
minute, from which point it decreases as the speed is increased. 
With the Albro-Hindley worm and wheel the maximum effi- 
ciency was found at 243 feet of rubbing per minute. With 
either form of gearing, the highest efficiency is to be found at 
a speed of rubbing of the surfaces in contact, which is different 
with different forms and proportions of gearing. The " Hind- 
ley screw" is a more efficient form of worm-gearing than the 
usually considered standard worm-gear, and the best form of 
gearing, by far, as respects efficiency of transmission, is the 
epicycloidal form of spur-gearing of the same total velocity- 
ratio, the loss of power in the last-named being but about one 
third or one fourth as great as in worm-gearing. 

The efficiency increased rapidly within ordinary limits as 
the load increased, in accordance with the law given in Chapter 



224 FRICTION AND LOST WORK. 

VII., and later tests of other special forms of worm-gearing gave 
efficiencies greatly exceeding the above. The common form 
of gearing is, however, superior to either of the other devices. 

Friction-gearing is usually made by turning grooves in the 
faces of two pulleys made for the purpose with heavy rims,, 
and so setting them that one may be forced into contact with 
the other, driving it by the friction of the surfaces thus forced 
into contact. The angle of the V-grooves so made is usually 
not far from 5.0 , with breadth to depth as 9 to 1, nearly. The 
coefficient of friction is about f = 0.16; but the pressure 
adopted is about equal to the effort transmitted. The "pitch" 
of the grooves is usually from J to f inches (0.6 to 2 cm.). 
The lost work is less than with a belt — in some cases by 25 or 
30 per cent. 

119. The Friction of Pump Pistons has been found by 
Daubuisson and later experimenters to be proportional to their 
diameters and to the pressure. 

The frictional resistance of hydraulic-press plungers was 
found by Hicks to be, when in good order and under mode- 
rately heavy loads, nearly equal to 5 per cent., divided by the 
diameter in inches, cupped leather-packing being used ; i.e., if 
the total friction-resistance be called F, the total load W, the 
diameter d, 

W 
F = 0.05 — r-, nearly. 

The depth of the collars used as packing and the length of 
the press-plunger have no sensible effect upon the friction, the 
resistance due to friction increasing directly as the load or the 
pressure, and inversely as the diameter of the cylinder. For 
pressures less than 500 lbs. per square inch (35 kgs. per sq. 
cm.) the friction rapidly increases with decreasing loads. Good 
lubrication may decrease this resistance very considerably. 

Clark gives, for new leather collars not well lubricated, F = 
o.tfdp, and for good lubrication and old collars F = o.^\dp r 
where/ is the intensity of pressure. 

Slide-valves of metal, on metal seats, are in steam-engines 
lubricated by the wet steam which passes them, and are re- 



EXPERIMENTS ON FRICTION— TESTING-MACHINES. 22$ 

lieved of pressure to a limited extent by the steam which finds 
its way between the valve and the seat. The value of /varies 
greatly for this case, but is usually taken as/ = 0.15 ; it actu- 
ally often rises to / == 0.25, or even to / = 0.5, and valve- 
stems are often broken. In ordinary working the lowest of 
the above values is probably quite high enough. 

Slide-blocks, or bars and guides, in machinery are to be cal- 
culated by the principles to be given for other cases of lubri- 
cated surfaces. If W is the total load on the piston, P the 
pressure on the guides, A their area, r the length of crank, / 
that of the rod, and Fthe speed of piston, 



the mean pressure is 



P=Wj;: ...... (1) 

p m = p 



07854^ 



the work of friction is 



MP — 0.617^ 

r 

= 0.7854 Py, nearly; ... (2) 



U=P m v = 0.7854^ 7;. • • (3) 



and the heat produced becomes 

U r 

H = -j = 0.001 Pv-j, nearly. . (4) 

120. The Friction of Fluids and of Semi-Fluids, such 
as gases, liquids, resins, and in some cases earth, follow laws 
varying greatly from those governing the friction of solids, and 
these laws have been already stated in Chapter II. The 
friction of liquids and of gases has been experimentally studied 
by many distinguished investigators. These researches con- 
firm the principles embodied in the mathematical analysis of 
the case. The friction of any fluid is found to be independent 
of the pressure, as first shown by Coulomb, who measured the 
friction of a rotating disk submerged in water, applying vary- 



226 FRICTION AND IOST WORK. 

ing pressures to the surface of the mass, and by many later 
observers who find the frictional losses of head of fluids tra- 
versing pipes, under different pressures, to be the same at the 
same velocities. 

The law that the resistance is, with velocity constant, 
directly proportional to the area of surface is almost axio- 
matic ; it is fully confirmed by experiment. It is found, how- 
ever, that where a body moves in a large mass of fluid, the 
friction of the leading portions of the surface of the moving 
body causes some motion of the adjacent fluid in its own 
direction, thus reducing the relative velocity, the velocity of 
rubbing, from forward aft, and correspondingly reducing the 
resistance of large bodies, as those of long ships. 

Low velocities are found to give variations from the law 
assumed in the theory, while high velocities more closely ac- 
cord with that law. This variation is only important for 
velocities considerably less than one foot (0.31 m.) per second. 

The smoothness or roughness of surfaces exposed to fluid- 
friction has been found to considerably affect this resistance. 
For all velocities usually met with in engineering, the ex- 
pression 

R = fA V" = f DA — , U = fA V 5 = f'DA V , 

given in Chapter II., may be adopted, where R and £/ measure 
the resistance and the work of friction, A is the area of rub- 
bing surface, D the density, V velocity of relative flow. 

121. The Flow of Gases is subject to modification by 
changes consequent upon variation of temperature due to fric- 
tion, and problems relating to such flow are therefore compli- 
cated with calculations of the effect of heat ; but where no heat 
is lost by conduction there is no loss of head by friction, ex- 
cept such slight losses as are due to the imperfectly fluid 
character of known gases. 

The loss of head may be taken as the same as for liquids, 
and the method of flow is similar. Unwin obtains for air 

7=0.005(1 + 3.6^), ...... (1) 



EXPERIMENTS ON FRICTION— TESTING-MACHINES. 227 

when d is expressed in inches, and the velocity is 400 feet per 
second or more, the data being obtained from experiments by 
M. Arson. Experiments at the St. Gothard tunnel give, for 
probably rougher surfaces, 

/= 0.0028(1 + ^) (1) 

122. The Friction of Liquids, as affecting the work of 
the engineer, is always a cause of lost work by resisting the 
relative motion of the liquid and some solid which is driven 
through it, as when a ship moves across the ocean, or which 
constitutes a channel along which the liquid is impelled. 

Fluid-friction occurring between the touching surfaces of a 
solid and a liquid is proportional, according to accepted authori- 
ties, to the area of surface of contact and to the density of the 
fluid, and is found, as already stated, to be nearly as the square 
of the velocity of their relative motion ; i.e., 



in which F is the measure of the resistance when f is the co- 
efficient of fluid-friction, D = the density of the fluid, A = the 
area of surface of contact, V— the velocity of flow, and g=. 
the measure of gravity = 32.2 feet per second, while h is the 

head due the velocity, and equal to — 

For iron pipes, according to Eytelwein, 

. 0.00144 
/=0.0056 + p^; 

or, according to Weisbach, 

j, s , 0.0043 

/ =0.00 3 6 + -^; 

and for average value, f =. 0.0064. 



228 FRICTION AND LOST WORK. 

The mean velocity of a stream of water, according to Prony, 
is 

771 + V 



v=V 



10.25 + V 



where v is the mean and V the maximum velocity of the 
stream as measured at the middle thread of its surface ; the 
difference between v and Fis due to friction. 
In flowing streams, according to Eytelwein, 

„ , 0.00136 
/= 0.00716 + r /-' t 



or, according to Weisbach, 

, 0.00023 
/= 0.00741+—- y— ; 

and an average value is /= 0.0076.* The value is somewhat 
variable. 

The method of variation of this friction depends both on 
the nature of the fluid and on the character of the surrounding 
solid surfaces. Froude found in salt water, and with surfaces 
of small area coated with tallow or with shellac varnish, that 
the resistance to the motion of ships, which in well-formed 
vessels is principally frictional, varies as V 1,m ; surfaces coated 
with tinfoil gave F oc F 205 . With surfaces of considerable 
area, the character of surface seemed comparatively unimpor- 
tant. 

The total loss of head, in any case of friction of water in 
orifices or pipes, may be taken as a loss of head equal to 



F— — F-— 

2g 2gA 



* Rankine, Applied Mechanics, § 638. 



EXPERIMENTS ON FRICTION— TESTING-MACHINES. 2 29 

in which 

F = 0.054 for an orifice in a thin plate ; 
F= 0.505 for an entrance into a pipe from a reservoir; 
F = 0.505 + 0-3 cos * + °- 2 3 cos8 * f° r a mouthpiece mak- 
ing the angle i with the side of the reservoir. 

Q is the quantity of water flowing and A the area of sec- 
tion of the channel. 

Where the ajutage has the form of the contracted vein, its 
cross-section at a distance radius from the side of the reservoir 
is of a diameter equal to 0.7854 the diameter at the side ; in 
this case the value of F becomes practically zero. 

lb 

In pipes and conduits, F = f.—r, 

in which expression /has the value already assigned ; /, b, and 
A are, respectively, the length, breadth, and area of cross-sec- 
tion of the stream. 

Substituting for -r, its value, the reciprocal of the hydraulic 

lb . „ ■ / 

mean depth, — = -j, we may write F — f~. 

Friction is somewhat increased by bends and " knees" in 
pipes ; and from Weisbach's experiments are deduced, for 
smooth bends, 

d 



'-7s?d»»+ Mm 



in which i is the angle through which the pipe is bent, r is the 
radius of the curve, and d is the diameter of the pipe ; for 
knees, i.e., rectangular or abrupt changes of direction, we find 

i i 

F= 0.0^ sin 2 — -4- 2 sin 4 — . 
yD 2 [ 2 

The values of f and / / in the expressions for fluid-friction 
vary with circumstances. The values obtained by Froude and 



23O FRICTION AND LOST WORK. 

other experimenters accord well with the following, as given 
for f and f in the simpler of the expressions given at the 
opening of Article 120: 

Painted iron (Unwin) 0.00489 0.00473 

Smooth, painted wood (Beaufoy) 0.00350 0.00339 

Iron ships (Rankine) 0.00362 0.00351 

Varnished surface (Froude) 0.00258 0.00250 

Fine sand (Froude) 0.00418 0.00405 

Coarse" " 0.00503 0.00488 

The resistance of ships is often expressed by the formula 
of Rankine, 

SV' J 



in which 5 is the area of " augmented surface" in square feet, 
V the speed in knots per hour, and C a coefficient, which 
ranges from 20,000 to 25,000 in full to fine vessels. The aug- 
mented surface is measured by the product of length, mean 
wetted girth, and a coefficient of augmentation obtained by 
taking the sum of unity, four times the mean of the squares 
of the sines of greatest obliquity of water-lines, and the mean 
of their fourth powers. 

Sudden enlargements and sharp bends often cause serious 
losses of head and of pressure. 

Notches discharge less than the quantity which should pass 
if no such loss as is above described takes place. For a rectan- 
gular notch, the volume discharged is 



Q = %cbd V2gd y 
= 5-35 <$d\ 

in which c is a coefficient usually not far from 0.6, b and d are 
the breadth of notch and the depth of stream issuing through 
it. If W is the width of the channel, 

b 
£ = 0.57 + 0.1-^, nearly. 



EXPERIMENTS ON FRICTION— TESTING-MACHINES. 23 1 

123. The Friction of Earth has been the subject of many 
experiments. The alteration in form and location of any mass 
of earth by the action of gravity, as has been seen (§ 41), is re- 
sisted by both friction and adhesion. Where the latter occurs 
to any considerable extent, as in clayey soils, a bank may even 
overhang its base at a measurable angle. Where adhesion is 
inappreciable, as in dry, sandy soil, the surface assumes a 
uniform slope at an angle with the horizontal which is the 
" Angle of Repose," the tangent of which measures the " Coef- 
ficient of Friction." The latter is also the limit of declivity 
assumed by any soil or earth in which, as is always liable to be 
the case, adhesion is destroyed by moisture or other cause. 
In calculations relating to the sustaining power of earth under 
foundations or the pressure upon a retaining-wall, the angle 
of repose, as obtained by direct experiment, must be known 
to insure safety. 

The angle of repose is in some cases liable to be reduced 
to a very small value by the presence of water, as in flooded 
quicksand or in saturated clayey earth. The least probable 
value should in such cases be assumed. In some cases the soil 
should be considered as a perfectly fluid mass of maximum 
density, and its pressure calculated as if it were a liquid. 

Calling cp the angle of repose, experiment gives the follow- 
ing values of cp and of/, the coefficient of friction, as obtained 
by Morin: 

Material. <j> / jr 

Stone and brick 30 to 35^ 0.6 to 0.7 1.7101.4 

Same on clay (dry) 27 0.50 2.0 

" " (wet) 18 0.33 3.0 

Earth 15 to 45 0.25 to 1. 00 i.oto4.p 

Sand and Gravel 40 to 48 0.8 to 1.1 0.9101.2 

Clay (wet) 18° 0.33 3.0 

" (damp) 45 1.0 1.0 

The following are values of the factors used in the equa- 
tions of Chapter II., §41, corresponding to several values of cp. 
The quantities in line (6) are especially interesting, as applying 
to foundations and to retaining-walls subject to jar or action 
of frost. 






232 



FRICTION AND LOST WORK. 



Values of Above Quantities. 





4> 


= 


o° 


15° 


3o° 


45° 


6o° 


(I) 


/ = tan <p 


= 


O 


0.268 


0.577 


I. OOO 


1.732 


(2) 


i 

— = cot <p 


= 


a 


3-732 


1.732 


I . OOO 


0.577 


(3) 


sin <p 


= 


o 


O.259 


O.50O 


0.707 


O.866 


(4) 


i + sin cp 
I — sin cp 


= 


i 


I.700 


3.OOO 


5.826 


13.924 


(5) 


/i + sin <p\* 
\i — sin cp) 


= 


i 


2.89O 


9.OOO 


33.94 


I93.8 


(6) 


i -4- sin 2 <p 
(i — sin cpf 


= 


i 


1-945 


5.00 


17.47 


97-4 


(7) 


sin cp 


= 


o 


O.081 


O.I33 


0.157 


O.165 


3 (i + sin 2 <p) 



The friction of earth on the pneumatic tubes used in laying 
foundations of bridges is given by Schmoll as below : 



Material of Tube. 



Sheet-iron, unriveted 
" " riveted . . 

Cast-iron, rough. 

Granite, hammered. 

Pine, sawn , 

Sheet-iron, unriveted 
" " riveted . . 

Cast-iron 

Granite 

Pine 



Soil. 



Gravel and sand. 



Sand. 



Dry. 



Start. Motion 



.402 

■397 
.368 
.427 
■409 
.536 
.727 
.564 
.647 
.663 



458 
491 
467 
537 
5ii 
631 

839 
606 
700 
734 



Wet. 



Start. Motion. 



•335 
.^68 

.365 
.410 
.411 
.366 
.516 
•474 
•473 
•579 



441 

548 
497 
480 

499 
325 
498 
370 
529 
479 



The friction of rest is here less than that of motion. It is 
not known whether this is a general rule for friction of this 
character, or due to circumstances peculiar to these experi- 
ments ; it is probably a case of fluid-friction, however, and that 
being the fact should follow its laws. It is well known that a 
load which will force an ordinary pile through soft bottom 
will not start it again if it is once stopped and the earth 
allowed to settle about it. 

It is advised by Trautwine that retaining-walls be given a 
thickness of from one third to one half their height ordinarily, 
accordingly as they are built of rubble and mortar or cement, or 
are built up dry, thus giving a factor of safety when the usual 
theory is adopted of from 7 to 20, asserting that a factor of 



EXPERIMENTS ON FRICTION— TESTING-MACHINES. 233 

safety of two is too small. The assumption introduced into the 
theory, by the Author, that the effect of friction may be the in- 
crease of pressure, instead of a decrease, permits the use of a 
reasonable factor; two may be used, four would be better. 

The maximum pressure allowable on foundations in earth 
is considered usually to be one or two tons, and in very com- 
pact soil sometimes four or six tons per square foot. Clay 
should carry from one to two tons. Uniform pressure should 
be secured if possible. 

124. Mixed Friction, or " mediate friction," as defined in 
Chapter II., arising from the resistance of solids in contact con- 
joined with the resistance of fluids to relative motion, has been 
frequently made a subject of investigation ; but it has rarely 
occurred that the bearing of the two methods of resistance upon 
each other and their resultant effect have been noted. Where 
the thickness of fluid interposed between two solids is great, as 
when a ship is under way in deep water, the resistance follows 
the laws of friction of fluids ; when the two solids are near 
each other, as when a vessel moves over shoals, the law begins 
to change ; and when they are in close proximity, as in the 
case of lubricated sliding or rotating pieces, the law becomes 
much more in accordance with that of friction of solids. 

Recent experimentors upon the friction of machinery have 
begun to note these variations. The total resistance in such 
cases is found by experiment to be a function of pressure, 
velocity, and temperature. 

When the rubbing-surfaces become dry, the variable part 
of these functions disappear and the law is reduced to that of 
friction of solids. 

125. The Friction of Lubricated Surfaces was made a 
subject of experiment by both Rennie and Morin, as well as 
by many later investigators. Their results are of compara- 
tively little value, however, in consequence of the fact that it 
was unknown until recently that the friction in such cases is 
greatly influenced by pressures, velocities, and temperatures, 
and because of the fact also that the experiments included but 
a limited range of conditions, and those were only such as are 
not most common in engineering. 



234 



FRICTION AND LOST WORK. 



Morin observed the great difference between the friction 
of rest and that of motion, and attributed this difference to 
the expulsion of the lubricant when the rubbing surfaces were 
relatively at rest. He thus accounted for the comparatively- 
great effort required to start machinery into motion. 

The following table presents the values of the coefficients 
of sliding friction measured by Morin, and the friction-angles 
corresponding to them, as determined for various conditions 
of surface : 

SLIDING FRICTION OF SOLIDS. 



Material. 



Brick on limestone 

Cast-iron on cast-iron, 

" on oak , 

Copper on oak 



Dry 

Slightly greased. 
Wet 



Leather on cast-iron 



" oak. 

i e a 



Oak on oak 



Oak on pine 

" limestone 

" hempen cord 

Pine on pine 

" oak 

Smooth granite on rough granite. 

Stone on dry clay 

" wet clay 

Wrought-iron on oak 



on wrought iron. 

" cast-iron 

" limestone.... 

Wood on metal 

" " smooth stone 

" " " earth 



Condition of Surfaces. 



Greased. 



Wet 

Oiled 

Fibres parallel 

" crossed 

" parallel, dry 

" crossed, dry 

" parallel, soaped 

" crossed, wet 

" end to side, dry 

" parallel, greased 
Heavily loaded and greased. 
Fibres parallel 

" on end 

" parallel 



Wet. 



Greased. 
Dry 



/• 



0.67 
0.16 
0.65 
0.17 
0.11 
0.28 
0.38 
0.12 
0.74 
0.47 
0.62 

o.54 
0.44 
0.71 

o.43 
0.07 
0.15 
0.67 
0.63 
0.80 
0.56 

o.53 
0.66 
0.51 

o.34 
0.62 
0.65 
0.28 



Friction 
Angle. 



33 5o' 
9° 6' 

33° 2 
9° 38" 
6° 17' 

15° 39 r 

20 49' 

6° 5 r 

3°° 30 

25 n r 

31 48' 

28° 22 r 

23° 45' 
35° 23' 
23° 16' 
4° 6' 
8° 45' 
33° 5o' 
32° 15' 
38° 40' 
29° 15' 
27° 56' 
33° 26' 
27 2' 
18 47' 
31 48' 
33° 2' 
15° 39' 
io° 46' 

26 i 

6° o' 
30° 7' 

18 16' 



These values are so greatly affected by variation of pres- 
sure, temperature, and velocity of rubbing, that this table has 
comparatively little value. More complete and useful tables 
will be given later. 



EXPERIMENTS ON FRICTION— TESTING-MACHINES. 235 

126. The Friction of Journals variously lubricated was 
made a subject of investigation by Rennie and by Morin, and 
has recently been experimentally studied by many engineers. 
The following are principally Morin's figures as obtained with 
journals of from 2 to 4 inches (5 to 10 cm.) diameter, and 
loaded with from 330 lbs. (150 kgs.) to 2 tons (or tonnes). 
The resistances were measured with a Morin recording dyna- 
mometer. The results are considered to be somewhat uncertain. 
As will be seen later, very much better conditions are probably 
attained in good practice with ordinary machinery. The values 
of f here given may be taken as fair figures for new journals 
lightly loaded. More extensive and more exact and useful 
determinations will be given in succeeding pages. Those here 
given are so greatly modified, as stated in the preceding article, 
by variations of speed, pressure, and temperature, that they 
cannot be taken as correct for general purposes. 



FRICTION OF JOURNALS. 



Material. 


Unguent. 


Lubrication. 


Intermittent. 


Continuous. 


Cast-iron on cast-iron 


Oil, lard, tallow .... 

Oil and water 

Asphalt 


O.07 to O.08 

O.08 

O.054 

O.14 

O.14 

0.07 to 0.08 

0.16 

0.16 

0.19 

0.18 

O.IO 

0.14 

0.07 to 0.08 
0.07 to 0.08 
0. 19 
0.25 

O.II 

0.19 

O.IO 

0.09 
0.12 

0.15 


0.03 to 0.054 




Unctuous 




Cast-iron on bronze 


" and wet.. . 
Oil, lard, tallow .... 
Unctuous 


0.03 to 0.054 




" and wet . . 

(slightly). . 

Dry 


t 

O.OgO 


Cast-iron on lignum-vitae . . . 


Oil, lard 

Unctuous (oil or lard) 

" (lard and 

erranhite} 


Wrought-iron on cast-iron . . 
Wrought-iron on bronze. . . . 

Iron on lignum-vitae 


Oil, lard, tallow .... 
Oil, tallow, lard .... 
Unctuous and wet . . 
" (slightlv). . 
Oil, lard 


0.030 to 0.054 
0.030 to 0.054 

% 


Unctuous 






Olive-oil 






Lard 




Bronze on cast-iron 

Lignum-vitae on cast-iron. . . 


Oil, tallow 

Lard 


0.030 to 0.054 


Unctuous 




Lignum-vitae on lignum-vitae 




0.07 







* Wear began. f Wood slightly greasy. % Wear commenced 



236 FRICTION AND LOST WORK. 

A large number of determinations, made under conditions 
more precisely defined and under circumstances more exactly- 
accordant with those of everyday practice, will be given here- 
after. It will be seen by reference to the theory of journals, 
that the resistance depends upon the method of fitting. It is, 
however, usually taken as F = fP, as for a journal fitting on a 
line. 

The value of f on grindstones has been found by Dr. Hartig 
to vary from / == 0.20 or f = 0.30 to / = 0.70 to / = 1.0 for 
light work and high speed and heavy work and slow speeds, 
respectively. 

Tests made on the machine of the Lake Shore and Michi- 
gan Southern Railway, and reported to the Master Mechanics' 
Association, are stated to have given the following results : * 

Fifty drops of each oil were used at one application, and 
the machine was driven at a speed corresponding to 35 miles 
an hour, until the temperature shown by the thermometer 
rose from 6o° to 200 F. (16 to 93 C). The total number 
of revolutions was as follows : 

Endurance of Oils— L. S. & M. S. RR. 



Castor 12.946 

Paraffine 11,685 

Mecca (black) 9,982 

Neat's-foot 8,277 



West Va 7,915 

Sperm 7,912 

Tallow 7,794 

Lard.. 7,377 



The most extended series of experiments of this character, 
and in some respects the most valuable obtained in this way, 
are those of Mr. A. H. Van Cleve.f The test-journal was 7 
inches long and 6 inches in diameter (17 cm. X 14 cm.), running 
in brass bearings, and driven by a 5-horse-power engine. The 
pressure was applied by a system of scale-beams, and the speed 
determined by a counter. The temperature was kept at from 
96 to ioo° F. (36 to 38 C), and was shown by a thermometer 
inserted in the bearing. A record was kept of the pressure, 
the speed, the quantity of oil used, and the power demanded 

* National Car- Builder, 1877. 

\ Scientific American, December 9, 1871. 



EXPERIMENTS ON FRICTION— TESTING-MACHINES. 2$? 



to turn the shaft. In a second series of tests, a journal was 
used 6 inches long and 2f inches in diameter (14 X 6 cm.) 

The results indicated that, in general, winter sperm sustains 
high pressures best ; that the mineral oils used only kept the 
journal equally cool when from 2 to 5 times as much oil was used 
as of sperm.* The pressure admissible varied nearly inversely 
as the velocity of rubbing, and the consumption of oil varied in 
a similar direct ratio. These experiments occupied fourteen 
months. The following table gives the principal facts: 

FRICTION OF 7" X 6" JOURNAL. (VAN CLEVE.) 



Oil. 


H. P. 


Rev. 

per M. 


Pressure, 
lbs. 


Tempera- 
ture. 
F. 


Gills of 

Oil. 
Per Hr. 


Relative 
Value. 


Winter Sperm -\ 

$ Sperm — \ Lard 

* " -i " 

i " — I " 


3-24 
to 

3.55 

2-45 
2.6r 

2.15 


125 
to 

131 
129 
129 
132 


7,000 

to 
7.500 
5.260 
5,600 
4,500 


96° 
to 

98 

97° 
97° 
96° 


O.68 

to 
0.S2 
O.84 
O.86 
0.76 


I. OO 

to 
O.9I 
O.69 
O.74 
O.60 



Winter Sperm, 



CAR-AXLE BEARING, 6" X 2f". 

..I 3.18 I 251 I 7,000 I 95' 



I 0.25 I 0.91 



LOCOMOTIVE AXLE. 



Winter Sperm. 



Lard. 







130 


7,000 


97° 


0.40 








100 


7,200 


94° 


0.26 








70 


8,000 


94° 


0.18 








60 


9,800 


94° 


0.14 








130 


7,500 


98° 


0.36 








IOO 


7.500 


96° 


0.25 








70 


8.000 


9i° 


0.19 








60 


9.500 


90 


0. 10 








130 


4.000 


78 


0.31 








IOO 


5,200 


75° 


0.18 








70 


5.500 


73° 


0. 12 





As early as 183 1 Nicholas Wood determined the coefficient 
of friction on old, well-worn axles, under conditions not fully 
specified, to be much less than those given in the table, as 
obtained by Morin, falling to about 0.02. Later German ex- 
periments, with pressures of 200 to 250 lbs. per square inch, 
gave, at 230 revolutions, f = 0.00891 to f= 0.013, and it was 



* A conclusion which is not true of all mineral oils. 



238 FRICTION AND LOST WORK. 

concluded that these values could be reduced. Still later 
experiments showed an increase of resistance in higher ratio 
than increase of load, and an increase with increase of 
velocity, while experiments at Hanover lead to the conclu- 
sion that, under loads of from 320 to 1250 lbs. (145 to 
564 kgs.) on the journal, the coefficient for iron axles 
lubricated with rape-seed oil and running in white-metal bear- 
ings is. 0.009 to 0.0099 ; that with gun-bronze bearings the 
figure becomes 0.014; that the value maybe taken as inde- 
pendent of the weight of load within usual limits ; that the 
area of the journal does not sensibly affect the resistance ; that 
resistance is practically independent of velocity of rubbing ; 
that grease gives a higher figure than oil for light loads, but 
the same under heavy loads.* As will be seen by the study 
of more complete results of experiment to be given later, these 
conclusions require some important modification. More cor- 
rect values of /"will be given in Chap. VII. Kirschweger ob- 
tained for railway axles running in Babbitt metal, f =. 0.009, 
and in bronze, f= 0.014. Bokelberg and Welkner obtained 
f = 0.003 to/"= 0.013 for low pressures and velocities and for 
high pressures and speeds respectively, gun-bronze giving the 
best results. 

The frictional resistance of mill-shafting has been determined 
by the very numerous and extended experiments of Mr. Samuel 
Webber. The pressures are here not very high, and Webber's 
values for the coefficient of friction average very nearly the 
same as the figures obtained by Morin. They are, for inter- 
mittent lubrication, 0.066, and for continuous oiling, 0.044. 
Morin obtained 0.075 an ^ 0.042. 

We may, as shown by analysis, adopt the following formulas 
for work of friction, U, and horse-power, H.P., required : 

[/= fWS, on flat surfaces ; (1) 

— 0.26/lVdR, on journals ; ....... (2) 

= ai 7$fWdR, on cylindrical pivots ; ... (3) 

= 0.026/lVdR cosec a, on conical pivots ; . . (4) 

== 0.1 J^fWdR sec a, on conical journals. . . . (5) 

*W. R. Browne, Railroad Gazette, August 16, 1878. 



EXPERIMENTS ON FRICTION— TESTING-MACHINES. 239 

And 

H. P. ■ = 0.00003/J^V, on flat surfaces ; (6) 

= 0.00000%/WdR, on cylindrical journals ; . . (7) 
== 0.00000 s/WdR, on cylindrical pivots ; . . . (8) 
= o.ooooo&f WdR sec a, on coned journals ; . . (9) 
= o.OOOOO$f WdR cosec a, on coned pivots. . (10) 

Mr. D. K. Clark* takes the values of/", from various sources, 
as averaging /= 0.07 and/= 0.043, for cases of ordinary and 
of free lubrication respectively, and thus gets 

Z/=o.oi%2WdR, for ordinary oiling; .... (11) 

= 0.01 12 WdR, for continuous oiling; . . . (12) 

H. P. = 0.0000005 WdR, for ordinary oiling; . . . (13) 

= O.OOOOOO33 WdR, for continuous oiling; . (14) 

the free supply giving a gain of 40 per cent. In these equa- 
tions, J^is the load in pounds, 5 the space in feet, R the revolu- 
tions per minute, d the diameter in inches, a the angle of the 
cone. 

127. The Size of Journals has been seen (Chap. II., Art. 
29) to be determined by the magnitude of the friction, only as 
to its length. The diameter is made sufficient to insure safety 
against springing and permanent distortion, and the length is 
determined by the limit of intensity of pressure allowable; 
while this limit is fixed, as will be seen more clearly hereafter, 
by the speed of rubbing and the temperature of the surfaces 
in contact. The usual maximum pressures, the pressure at 
which the limit of safety against abrasion is approached, has 
been given as 500 or 600 lbs. per square inch (35 to 42 kgs. 
per sq. cm.) for iron crank-pin journals, and as about double 
these figures for steel. It is, however, variable with change of 
speed, etc. The maximum pressure on timber, as on the 
launching-ways of vessels, is below one tenth that for iron. All 
bearing-surfaces should have sufiicient area at least to reduce 
the intensity of pressure below these figures, and should be 
increased beyond this extent in the manner given below, with 

* Manual, p. 763. 



240 FRICTION AND LOST WORK. 

increase of speed, or for journals subjected to unintermitted 
pressure. 

The two surfaces usually differ — the one being hard enough 
to bear the maximum pressure without change of form, and 
the other being less hard, in order that it may not abrade the 
first. With such an arrangement, the surfaces, if properly 
cared for, take a fine smooth, mirror-like polish, and give a 
minimum frictional resistance. Cast-iron surfaces are usually 
less satisfactory than good wrought-iron, although where the 
areas can be made large, cast-iron bearings work very satisfac- 
torily, and homogeneous and moderately hard steel is vastly 
better for journals than iron. A pressure of 800 lbs. to the 
square inch (56 kgs. per sq. cm.) can rarely be attained on 
wrought-iron at even low speeds, while 1200 lbs. (85 kgs. 
per sq. cm.) is not infrequently adopted on the steel crank- 
pins of steamboat engines; but double this pressure has been 
reached on locomotives, at the instant of taking steam. Seven 
to nine thousand pounds pressure per inch is reached on the 
slow-working and rarely moved pivots of swing-bridges. In 
practice with heavy machinery, higher pressure than 600 and 
1000 lbs. per inch (42 to 70 kgs. per sq. cm.) on iron and on 
steel are rarely adopted, and in general practice we make the 
pressure less as the speed is greater, since the amount of heat 
developed is directly a measure of the amount of work done in 
overcoming friction, and is proportional to the speed as well as 
to the pressure. Reciprocating motion in journals compels the 
adoption of greater length than continuous revolution. Slowly 
moving journals are often but one diameter in length ; fast- 
working journals are sometimes 6 and 8 diameters long. Under 
steady pressure, this length must be greater than under inter- 
mitted loads. 

By watching the behavior of the journals of the engines of 
naval steamers in 1862, the author determined the following 
formula for the size of journals for such engines and for sta- 
tionary steam-engines:* 

PV 



1 = 



6o,oood 



* Materials of Eng., vol. i. 



EXPERIMENTS ON FRICTION— TESTING-MACHINES. 24 1 

in which / is the length of the journal in inches, P the average 
load in pounds, and V the velocity of rubbing in feet per 
minute ; d is the diameter in inches. Rankine published, in 
1865, the following as applicable to locomotive practice: 

l= P(V+2Q) 

44,800^ 

These are intended for iron journals ; those of steel may 
sometimes work well if of one half the length given by the 
formulas. 

The length being known, the mean pressure per square inch 
admissible is within the limits above given, 

60,000 ,_, 
p — — — — (Thurston). 

44,800 . 

* = T+~Z6 (Rankine). 

Where journals are exposed to dust, as in locomotives, or to 
unintermitted pressure, it is advisable to make them of greater 
length than where they are fully protected. This difference is 
observed in the two formulas just given. The best makers of 
mill-shafting make the journals about four diameters long. 

The expressions above given can only be taken as correct 
for such cases as are familiar to the engineer as representing 
good current practice. They are subject to great variation, 
with variation of condition and kind of surface, temperature, 
nature of the lubricant, etc., etc. 

For rapidly revolving pivots, lower pressures and corre- 
spondingly increased areas of surface must be usually adopted. 
Fairbairn would restrict pressures, in this case, to less than 
240 lbs. per square inch (18 kgs. per sq. cm.), which he thinks 
a critical pressure. Trautwine takes pressures 40 per cent, 
lower for iron "steps," and 25 per cent, higher for steel — 
both to be used for general mill-work. Railway turntable- 
pivots, and those of drawbridges, which turn exceedingly 
slowly, sometimes work under pressures approaching the elastic 



242 



FRICTION AND LOST WORK. 



limit of the metal. Chilled iron and hardened steel work well 
if properly cared for, under loads of 6000 lbs. per square inch 
(422 kgs. per sq. cm.) when kept well lubricated. 

In all these cases ordinary methods of oiling are assumed. 
Where the oiling is intermittent, the pressure intermitted, the 
speed of rubbing small, and the lubricant fluid, these limits 
should never be exceeded ; if, on the other hand, the lubrica- 
tion is very free, as with the oil-bath, the pressure intermitted 
or reversed, as on crank-pins, the speed of rotation of journal 
high enough to force the lubricant between the surfaces, and 
the latter at the same time of good "body," much higher 
limiting pressures may be sometimes attained. A steady, 
unintermitted pressure will not permit maximum intensity of 
pressure to be maintained. 

The experiments at the Brooklyn Navy Yard, made under 
the direction of the Bureau of Steam Engineering, and under 
these conditions, were reported to indicate the following limits 
of pressure for a velocity of rubbing of about 200 feet (60 m.) 
per minute, and a temperature of 116 F. (47 C), the pressure 
and speed being unintermitted. 



Pressure. 

Lbs. per Kgs. per 

sq. in. sq. cm. 



Oil. 

Summer Sperm Oil 86 6 

Winter Sperm Oil 70 5 

Winter Lard Oil 62 4.3 

Tallow Oil 50 3-5 



Pressure. 
Oil. Lbs. per Kgs. per 
sq. in. sq. cm. 
Heavy Mineral Oil 73 5.1 

Light Mineral Oil 65 4.5 

Paraffine Oil 55 4 

Mineral and Fish Oil... .48 3.5 



These figures are very much smaller than would be given 
by either of the rules above given, which at 200 feet would be 
from 200 to 300 lbs. per square inch (14 to 21 kgs. per sq. cm.). 
In other words, the apparent factor of safety is here at least 
2 or 3 for the best oils. The rules reduced to this basis would 
read 

15000 



V 



nearly, 



for sperm-oil. As previously given, however, they have been 
adopted in the design of many steam-engines and other 
machines, and have given satisfactory results. The adoption 



EXPERIMENTS ON FRICTION— TESTING-MACHINES. 243 

of the latter will give good results for light machinery, but would 
produce journals of impracticable size if used for heavy work. 

The pressure at which the film of oil is displaced and the 
friction becomes altered from liquid friction to mixed, or 
" mediate," friction by contact of the metals, varies greatly 
with different oils and at different speeds, and is not exactly 
known for any one lubricant. These pressures are perhaps 
not far different from those last given. Mr. C. N. Waite sup- 
poses this point to be reached with a pressure of about 84 lbs. 
per square inch (6 kgs. per sq. cm. nearly) with neat's-foot oil, 
one half this figure with lard, 70 lbs. (5 kgs.) with sperm, and 
deduces the conclusion that a light paraffine-oil is best for low 
pressures and a heavy mineral oil for heavy loads. This point 
varies, however, very greatly with velocity of rubbing, becom- 
ing as a rule greater as the speed increases. It is also, as 
already stated, very much greater where the pressure is inter- 
mitted, as on crank-pins of steam-engines, and less with vibrat- 
ing journals, as on the " beam-centres " of engines having 
" working-beams." 

128. Machines for Testing Lubricants are used in the 
most important of all the tests to be applied to determine the 
precise value of a lubricating material, and in that which most 
completely and satisfactorily reveals that value, the machine 
being specially constructed for the purpose. 

In order to determine precisely what oils are adapted to any 
special purpose, or to ascertain for what uses any oil is best 
fitted, it is necessary to make an examination of the lubricant 
while it is working under the specified conditions. That is to 
say : The oil should be put upon a journal of the character of 
that on which it is proposed to use it, and, subjecting it to the 
pressure proposed, running it at the speed that the journal is 
expected to attain ; its behavior will then show conclusively 
its adaptability to such an application. While running, it is 
necessary to measure the friction produced, and to determine 
its coefficient, which, as we have seen, is its measure, as well 
as to be able to note its durability and the rise in temperature 
of the bearing. These qualities being determined and recorded, 
all is known of the oil that is needed to determine its lubricat- 



244 FRICTION AND LOST WORK. 

ing power, and its value for the purpose intended. A number 
of such machines have been invented, although but two or 
three are in use. 

One of the oldest is that of McNaught. It consists of two 
disks. The upper one is loose ; the lower one is turned by a 
pulley on its spindle. The oil is interposed between the disks, 
and the friction causes a tendency on the part of the loose 
disk to turn with the other. This tendency is resisted by a 
pin on its upper side coming in contact with the short arm of 
a bell-crank lever, the long horizontal arm of which carries a 
weight which can be adjusted to measure the friction. 

The oil to be tested is placed between these two disks. As 
the lower one turns, the friction between them carries the 
upper one with it, but its motion is restrained by a pin, which 
comes in contact with another pin, in the end of the arm of 
a T-lever. A movable weight slides on the arm, on which is a 
scale to note its position. A counterweight is attached to 
the opposite end of the lever, so as to afford the means of a 
more delicate adjustment. It is evident that the resistance due 
to the friction between the two disks may in this way be very 
readily measured by the position of the weight. 

Napier's machine consists of a wheel, of which the smooth, 
wide rim is pressed by a brake-block, which is forced against it 
with any desired amount of pressure by the action of weighted 
levers. The effort of the wheel to carry the block around is 
resisted by another weighted lever, and by it the friction is 
measured, as in the later machine of Riehle. 

The machine of Messrs. Ingham & Stapfer consists of a shaft 
running in two bearings and carrying a third journal between 
them. This latter has adjustable bearings, which are set up 
to any desired pressure by weighted levers. A thermometer 
in the top brass enables the heating of the bearing to be ob- 
served. A later modification of this machine is seen in that of 
Ashcroft. In this machine the friction cannot be measured ; 
but the durability of an oil and its effectiveness in keeping a 
bearing cool can be observed. A somewhat similar but much 
larger machine has been used at the Brooklyn Navy Yard 
several years. 



EXPERIMENTS ON FRICTION— TESTING-MACHINES. 245 



The work done on the Ingham & Stapfer machine is some- 
times plotted as in the accompanying diagram : 



,::') 



r:n 



KEY. WW ^U- 00 i 5 000 2Q.Q0.O 25000 3000.0 -35000 40000 45000 5.0000 55000 6U0OU 65000 700 

Fig. 36. — Oil Test. Heat and Work. 



K 



J39 



The two dotted lines show the behavior of two different 
samples of oil under test. The line of large dots shows an 
excellent quality of prepared and purified sperm, that, starting 
at a temperature of 6j° F. (i9°.5 C), has with 70,000 revolu- 
tions only attained 176 (8o° C.) ; while the other, an indifferent 
mixed oil, attains 200° (93°. 3 C.) with only 19,000 revolutions. 
By means of such a diagram a permanent record of all tests 
can be kept for future guidance. 

The value of the lubricant is assumed (improperly) in the 
use of this machine to be determinable simply by observing 
its durability and its effect upon the thermometer. In making 
experiments of this kind, Mr. W. H. Bailey proposes that all 
should begin at the same standard temperature — say 6o° F. — 
and should terminate at the same point, which he would make 
200 . He enters the data, as obtained, on a record-sheet thus 
arranged : 



Name of Oil. 



Price. 



Total Rev. 
to 200 F. 



Temp, of 

Atmosphere. 



Rev. per Degree. 



In a test thus made to determine the gumming of oils, 
Wheeldon obtained the following table : * 



* Lecture by Mr. W. H. Bailey, Manchester, G. B. 



246 



FRICTION AND LOST WORK. 



TESTS OF OIL ON BAILEY'S MACHINE. 

Resistance to Oxidation. ( Wheeldon.) 





Name. 


Price. 


Rev. 


Temperature. 


Elevation 
of Temp. 


Rev. per 
Degree. 


First day 1 

Second day 2 


No. I Ox. 


5/6 


13,005 

11,787 


From 8o° to 200° 
" 78 to 200 


120° 
122° 


108 
97 


First day 3 

Second day 4 . . . . 


Sperm. 


9/0 


16,044 
13,104 


From 65 ° to 200 
" 62 to 200° 


135° 
138° 


II 9 
95 


First day 5 

Second day 6 


Mineral(?) 


3/6 


11,831 


From 65 ° to 200 


135° 


88 









1 First trial; new oil. 2 No fresh oil added. 3 First trial; new oil. 4 No 
fresh oil added. 5 First trial. 6 Second trial; after standing 24 hours the bear- 
ings were found glued to the test-journal, and the machine refused to start. 



The last of these trials could not have been made with an 
oil of the kind indicated by the name given. Mineral oils do 
not gum ; this was undoubtedly a mixed oil of poor quality. 

The Zeitschrift deutcher Ingtnieure, 1871, gives the follow- 
ing: 

Oil. Price per cwt. Rev. Relative Cost. 

Refined Rape-seed $11 25 69,975 100 

Mineral 750 41,850 111.4 

Impure Rape-seed 9 60 26,392 225.9 

Lieut. Metcalfe, of the Ordnance Corps, U. S. A., in experi- 
ments made at the Frankford Arsenal* in 1873, on axle and 
trunnion friction, has adopted Rankine's method f of noting 
the time required by a fly-wheel running loosely on a shaft to 
lose a given quantity of energy while stopping under the 
opposing efforts of its own inertia and the frictional resistance 
of its lubricated bearing on the stationary axle. From this he 
deduced the coefficient of friction thus : 

The energy thus destroyed is 

rr Mk " . 



* Ordnance Notes No. LXXXIV. Washington, July 15, 1878. 
f Machinery and Millwork, p. 397. 



EXPERIMENTS ON FRICTION— TESTING-MACHINES. 2tf 

(W\ 
in which M is the mass 1 — J of the wheel, k its radius of gyra- 

tion, and a is the initial angular velocity. 

The work of resistance by friction is U = U, and is meas- 
ured by 

U — 2Fnrn = a 

2 

and 

F— , 

471m 

in which Fis the effort of friction resisting motion, r the radius 
of the shaft or journal, and n the total number of revolutions 
made while stopping. The mean velocity a' is one half the ini- 
tial velocity a. Then 

_, Mk'a 2 ^Mk'nn 



47trn ~ f ' 

where t is the time of retardation in seconds. 

F F _ 4k?7tn _ n 
f ~ W~ Mg ~ ~rfg ~ I' 

in which last expression C is a constant to be determined for 
any wheel used. 

In Metcalfe's experiments the pressure was about 100 
lbs. per square inch (7 kgs. per sq. cm.), and whale-oil gave 
f= 0.015 to/= 0.016, sperm-oil, 0.088 ; castor-oil, 0.028; axle- 
grease, 0.030. 

The average revolutions were 53 per minute. 

This affords a very convenient method of comparing the 
values of lubricants used upon the wheels of vehicles ; the 
wheel itself may be used as the storer and restorer of the energy 
expended in friction. 

129. The Ashcroft and Woodbury, the Wellington, the 
Tower, and the Riehle Machines for testing oils are improve- 
ments upon the earlier testing-machines. All embody provi- 
sions for ascertaining the value of the coefficient of friction. 



248 



FRICTION AND LOST WORK. 



The Ashcroft machine is a modified Ingham & Stapfer 
instrument, as seen in Fig. 37. 

It is operated in the same manner. The illustration shows 
the test-arbor, weighted lever producing pressure, the ther- 
mometer indicating changes of temperature, and a dial show- 
ing the friction-resistance. The oils tested are compared by 
noting the rise of temperature during test as already described, 




the maximum allowed being taken usually at a little below the 
boiling-point of water. 

Mr. Woodbury has improved the Nasmyth machine.* 
The machine is shown in perspective in Fig. 38. 
The lower disk is secured upon the top of an upright shaft, 
its top being an annulus, ground to a true plane surface. Upon 
this rests the upper disk, which is a hollow ring of hard compo- 
sition. 



* Trans. Am. Soc. Mech. Engrs., vol. vi., November, 1884. 



EXPERIMENTS ON FRICTION— TESTING-MACHINES. 249 

A partition divides the interior of the hollow ring forming 
the upper disk, and water can be introduced through the con- 




Fig. 38. — The Woodbury Machine. 

necting tubes to control the temperature of the disks or to re- 
tain the heat of friction. The sides and top of the upper disk 
are surrounded by a case of hard rubber, and the space is filled 
with eider-down. 



250 FRICTION AND LOST WORK. 

Ice-water is used to reduce the temperature of the disks to 
nearly the freezing-point of water, and the friction is noted at 
each degree of rise in temperature. 

A tube of thin copper, closed at the bottom, reaches through 
to the bottom of the disk, and a thermometer with its bulb 
placed within this tube indicates the temperature of the fric- 
tion-surface. A tube leading through the upper disk conducts 
the lubricant under trial to a recess in the middle of the lower 
disk. The upper end of this tube, being of glass, exhibits the 
supply and rate of feeding of the oil. As the friction of a jour- 
nal depends quite largely upon the method of lubrication, uni- 
formity in the manner of supply is of the utmost importance. 

The axes of the upper and lower spindle do not coincide, 
but are on parallel lines about one eighth of an inch from each 
other. This prevents the surfaces from wearing in rings, be- 
cause the same points are not continuously brought in con- 
tact with each other. 

A counter records the number of revolutions made during 
any given time. 

The dynamometer on the right-hand side of the machine 
consists of segments and pinions multiplying the deflection of 
a steel bar, and indicating the stress necessary to produce such 
deflection by the position of the hand on the dial. When the 
machine is in operation the lower disk is revolved, and tends 
to carry the upper disk around with it, by a force equal to the 
friction due to the lubricant between the disks. 

The frictional resistance is thus obtained : The reading on 
the dynamometer indicates the force of a couple whose arm is 
the length of the lever projecting from the upper disk, and 
this couple is opposed by a couple of equal moment, of which 
the dimensions of the frictional surface form the data for com- 
puting the arm, and the frictional resistance of the lubricant is 
the unknown quantity. 

The coefficient of friction is deduced from the data of ob- 
servation in the following manner: Let 



W = Weight on disks, lbs 
r 2 ■= Outei 
r, = Inner 



r 2 — Outer radius of fractional contact, feet. 



EXPERIMENTS ON FRICTION— TESTING-MACHINES. 2$ I 

r = Radius of any infinitesimal ring or band of the fric- 

tional surface, feet. 
N = Number of revolutions per minute. 
F = Reading on dynamometer, lbs. 
L — Length of lever arm of upper disk, feet. 
f = Coefficient of friction. 

Suppose that the annular surfaces of the disk be divided 
into an infinite number of elementary areas by equidistant 
circles and radial lines, then will 

Width of elementary band = dr. ...... . (i) 

Angle between two successive 

radial lines - = d6. ....... (2) 

Length of arc between two radii — rdd (3) 

Elementary area = rdrdd (4) 

Area of annulus = n{f — r*) (5) 

W 

Pressure per unit of area = — 7— , =7. .... (6) 

Wrdrdd 
Pressure on elementary area = — 7— 2 ^. .... (7) 

- . . f Wrdrdd 

Friction on elementary area = , a 57. .... (8) 

J 7t(r 2 — r?) v J 

Moment of friction on elementary area 

_ fWr'drdd 
~ n(r: - r;) ^ 

fW f*r 2 p*ir 

Moment of friction on entire disk = -jA =r / / rdrdd.iio) 

27tfW i-fH* 

Integrating —■—-—„ —\ . . (n) 



252 FRICTION AND LOST WORK. 

2fW(r 3 — r 3 ) 
Substituting the limits = — (^~ — *\- * ' ' ( I2 ) 

31/ 2 mJ 

. . . 4/7T^Mr 2 3 -0 ' N 

Work of friction per minute = r~^_ — n — * • (*3) 

3v 2 ' 1 ) 

The work of the dynamometer = 2nLFN. ..... (14) 

The friction equals the resistance; hence 

«^w* — <,) 

/_ 2W(r;-ry 

= aF-^W; (16) 

in which the constant coefficient may be easily determined by 
each machine. 

The work done by this machine will be referred to at some 
length in the succeeding chapter. 

In the construction of the Riehle machine, which is shown 
in Fig. 39, the inventors have introduced a "balanced" weigh- 
ing arrangement, and the combination, first used by the Au- 
thor, of a device for indicating the coefficient of friction with 
those for determining pressure and velocity of rubbing. 

The counter-pulleys admit of running the journals at dif- 
ferent speeds, and any pressure can be applied up to 2200 
lbs. (1000 kgs.). The thermometer and counter indicate the 
heat of the journal during the different stages of the testing, 
and the number of revolutions made by the journal. The 
coefficient of friction can be accurately determined by observ- 
ing the pressure and friction as indicated by the beam, in 
connection with size of journal. The beams are graduated 
like scale-beams, and balanced. One weighs the pressure pro- 
duced by the wheel and screw on the journals, one is used as 
a counterbalance, while the third measures the friction pro- 
duced when the machine is in motion. 



EXPERIMENTS ON FRICTION— TESTING-MACHINES. 253 

130. Thurston's Lubricant-Testing Machine. — The ma- 
chine devised by the Author was, so far as he is aware, the 
first in which it was made possible to obtain from indices on 
the machine measures of the velocity of rubbing and speed 
of revolution, the total pressure and the intensity of pressure 
on the journal, the temperature and the friction, and easily to 
determine the exact value of the coefficient of friction. The 
Author, some time previous to the year 1872, found that the de- 




Fig. 39. — The Riehle Machine. 

termination of the amount of frictional resistance had been sel- 
dom attempted, but that the simple measurement of the heating 
by means of machines of the Ingham & Stapfer class had been 
relied upon alone, and that results obtained were of value only 
by comparison. He therefore endeavored to devise a machine 
which should not only exhibit the heating of a lubricated jour- 
nal, under pressures and speeds variable at will, but one that 
should also give at the same time and with accuracy the more 
delicate but much more important measure of the friction. 
It was desirable that the machine should give not only a 



254 



FRICTION AND LOST WORK. 



measure of the resistance due to friction, but an exact meas- 
ure of the relation which that resistance bears to the total 
load on the journal ; in other words, it should give, directly 
and precisely, the value of the " coefficient of friction. " 

The construction of this machine is shown in Figs. 40 
and 41, below. 

At F is the journal on which the lubricating material is to 
be placed for test. This journal is carried on the overhung 
extremity of shaft A, which is sustained by the journals BB\ 
on a standard, D, mounted on a base-plate, E. The shaft 





Fig. 40. — Thurston's Machine. 



Fig. 41.— Thurston's Machine. 



is driven by a pulley, C, at any desired speed. A counter is 
placed at the rear end of this shaft, to indicate the number 
of revolutions. The shaft is usually driven at a fixed speed, 
corresponding to a velocity of rubbing surfaces approximating 
that of the journals on which it is proposed to use the oil. 
The testing-journal, F, is grasped by bearings of bronze, GG\ 
and with a pressure which is adjusted by the compression of a 
helical spring, /. This spring is carefully set, and the total 
pressure on the journal and the pressure per square inch are 
both shown on the index-plate, N, by a pointer, M. Above 



EXPERIMENTS ON FRICTION— TESTING-MACHINES. 2$$ 

the journal is a thermometer, Q, of which the bulb enters a 
cavity in the top " brass," and which indicates the rise in tem- 
perature as the test progresses. 

The "brasses," thermometer, and spring are carried in a 
pendulum, H, to which the ball, /, is fitted ; and the weights 
are nicely adjusted, and, as nearly as may be, in such a man- 
ner that the maximum friction of a dry but smooth bearing- 
shall just swing it out into the horizontal line. The stem, 
KK ', of the screw, which compresses the spring, projects from 
the lower end of the pendulum, and can be turned by a 
wrench. A pointer, 0, traverses an arc, PP', and indicates 
the angle assumed by the pendulum at any moment. This 
angle is large, with great friction, and very small with good 
lubricating materials. This arc is carefully laid off in such 
divisions that, dividing the reading by the pressure shown 
on the index, A 7 ", gives the corresponding coefficient of fric- 
tion. 

The figures on the arc are the measure of the actual resist- 
ance of friction on the surface of the journal. Dividing this 
frictional resistance by the total load gives the value of the 
coefficient. As there is no intermediate mechanism, this meas- 
ure is obtained without possible error ; and, as the resisting 
moment changes very rapidly at low angles, great precision of 
measurement is obtained, as will be seen when the results of 
experiment are given. The machine can also be arranged to 
give readings of this coefficient directly. 

The theory of the machine is as follows : Let 

R = radius to centre of gravity of pendulum ; 

F = effort due to weight of arm ; 

r = radius of journal; 
/ = length of journal ; 

W= weight of pendulum complete ; 

P = total pressure on journal ; 

p — pressure per square inch of longitudinal section ; 

T= tension on spring; 

6 = angle between arm and a perpendicular through axis ; 

f = coefficient of friction ; 

Q = total friction. 



256 FRICTION- AND LOST WORK. 

When Q is equal to 90 , 

FR=-Qr. ....". . . , (1) 

And when any other angle, 

FR sin 6 = Qr. ........ (2) 

Solving equation (2) with respect to Q, 
„ FR sin 

Q = — — ■ ■ - - - . . (3) 

The coefficient of friction is 

_ Q FRsind 
f =J=-~7P~- •■-••- (4) 

The pressure per square inch is 

P _ 2 T+W 
^~4lr~ 4/r ' •••••• (5) 

From this last equation the graduations on the right-hand side 
of the index-plate are deduced. 
From the equation 

N = 4i>lr ........ (6) 

the numbers on the left-hand side are determined. 

By substituting in equation (1) the value of Q, in terms of 
the coefficient and total pressure, from (4) it becomes 

FR=f{ A plr)r . (7) 

Solving with respect to f, equation (7) becomes 

FR 

f=JL> ( 8 ) 

Aplr 

From the numerator of the second number of equation (8) 
the graduations on the arc are deduced. 

In applying the foregoing equations to the machine shown 



EXPERIMENTS ON FRICTION— TESTING-MACHINES. 2$J 

in the engraving, the following numerical values may be given 
to the respective symbols : 

F= 2.5 lbs.; R— 10 in.; r = .625 in.; /= 1.5 in.; 4/r = 3.75 
sq. in.; w = 6 lbs. Also, a compression of if inches of the 
spring corresponds to a tension of 100 lbs. ; hence, for each 
pound's tension the spring will be compressed .01375 of an inch. 

The graduations on the right-hand side of the scale are 
obtained from equation (5) : 

2T+W 
* = -W~ (4) 

The first graduation will naturally be that value of / when 
T is equal to o, which value is 1.6. 

The speed of the machine, when the belt is upon the largest 
pulley of the cone, C, should be that which will give at the 
surface of the testing-journal the least speed of rubbing, 
which is expected usually to be adopted. 

The figures on the arc PP ', traversed by the pointer O y 
attached to the pendulum, are such that the quotient of the 
reading on the arc PP', by the total pressure read from the 
front of the pendulum at MN, gives the " coefficient of fric- 
tion," i.e., the proportion of that pressure which measures the 
resistance due to friction. 

A printed table furnished with, each machine gives these 
coefficients for a wide range of pressures and arc-readings. 

To determine lubricating quality, remove the pendulum 
HH from the testing-journal GG f , adjust the machine to run 
at the desired pressure, by turning the screw-head K project- 
ing from the lower end of the pendulum, until the index M 
above shows the right pressure, and adjust it to run at the 
required speed by placing the belt on the right pulley, C. 

Next throw out the bearings, by means of the two little 
cams on the head of the pendulum, H, in the small machine, 
or by setting down the brass nut immediately under the head 
in the large machine ; then carefully slide the pendulum upon 
the testing-journal, GG', and at the same time see that no 
scratching of journal or brasses takes place. 

Oil the journal through the oil-cups or the oil-holes, set the 



258 FRICTION AND LOST WORK. 

machine in motion, running it a moment until the oil is well 
distributed over the journal. Next stop the machine; loosen 
the nut or the cams which confine the spring, and, when it is 
fairly in contact and bearing on the lower brass with full pres- 
sure, turn the cams or the brass nut fairly out of contact, so 
that the spring may not be jammed by their shaking back 
while working. Start the machine again and run until the 
behavior of the oil is determined, keeping up a free feed 
throughout the experiment. 

At intervals of one or more minutes, as may prove most 
satisfactory, observations and records are made of the tempera- 
ture given by the thermometer, Q, and the reading indicated 
on the arc P, of the machine, by the pointer O. When both 
readings have ceased to vary, the experiment may be termi- 
nated. 

The pendulum is then removed, the pressure of the spring 
being first relieved, and the journal and brasses are cleaned 
with exceedingly great care; care is taken to have no particle 
of lint on either surface, or any grease in the oil-cups or oil- 
passages. 

The journal may be cleansed, after each test, either with 
alcohol, gasoline, or benzine. The effect of an oil is often felt 
in successive tests, long after starting with a new lubricant. 

A comparison of the results thus obtained with several oils 
will show their relative values as reducers of friction. 

Steam-cylinder lubricants are tested upon bearings heated 
to a temperature corresponding to any desired steam-pressure. 
When the maximum temperature has been attained the flame 
is removed, and the behavior of the oil noted as the tempera- 
ture falls to 212 F., which corresponds to atmospheric pres- 
sure or to zero on the steam-gauge. Any effervescence or 
excessive friction at the higher temperatures condemns the 
lubricant. It is the custom to take the average of the coeffi- 
cients of friction for temperatures ranging from 340 F. — cor- 
responding to a gauge-pressure of 104 lbs. — to 21 2° F. 

In each case the results are recorded in tables on the blanks 
(of which a copy is given on the next page) which are sent 
with the machine, and which exhibit — 



EXPERIMENTS ON FRICTION— TESTING-MACHINES. 259 











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260 FRICTION AND LOST WORK. 

(i) The pressure and speed of rubbing at each trial. (2) The 
observed temperatures. (3) The readings on the arc of the 
machine. (4) The calculated coefficients of friction. 

At the end of the trial the average and the minimum co- 
efficients are entered, and the total distance rubbed over by the 
bearing surfaces. 

To determine the liability of the oil to gum, the bearings 
are lubricated with a definite quantity of the oil, and the ma- 
chine run a certain number of revolutions. The temperature 
of the bearings and the friction at the end of this period are 
noted. Both journal and brasses are then removed, placed 
under a glass receiver, which excludes the dust yet permits the 
entrance of air, and are left there for any desired length of 
time, as for one day. At the end of that time the bearings 
are replaced in the machine, and the latter is driven until the 
temperature of the bearings is the same as at the previous 
trial ; the friction is then again noted. Any increase of fric- 
tion above that previously observed must be due to the gum- 
ming of the lubricant. For the machine described, the stand- 
ard quantity of the lubricant is 16 milligrammes, which is ample 
to afford perfect lubrication of the bearing surfaces during the 
trials. The number of revolutions at the first trial is often 
5000; it may, however, vary considerably without affecting 
the results, so long as it is too small to affect the wearing 
qualities of the lubricant, as within this limit the friction 
remains constant with a constant temperature. Changes in 
temperature and friction always accompany each other; it is 
for this reason that great care is taken to obtain the same 
temperature of bearing at each trial. 

To determine durability, proceed as in determining the fric- 
tion, except that the lubricant should not be continuously sup- 
plied, but should be fed to the bearing a small and definite 
portion of time — as a drop or two for each two inches length 
of journal. Extreme care should be taken that each portion 
actually reaches the journal and is not lost, either in the oil- 
hole or by being wiped off the journal, and that the portions 
applied are exactly equal. When the friction, as shown by the 
pointer O, has passed a minimum and begins to rise, the ma- 



EXPERIMENTS ON FRICTION— TESTING-MACHINES. 26 1 

chine should be carefully watched, and should be stopped, 
either at the instant that the friction has reached double the 
minimum, or when the thermometer indicates 212° F. ; or 
another portion of the lubricant should be then applied to the 
journal. 

This operation should be repeated until the duration of 
each trial becomes nearly the same ; an average may then be 
taken either of the time, of the number of revolutions, or of 
the distance rubbed over by the bearing, which average will 
measure the durability of that lubricant. Next carefully clean 
the testing-journal, and proceed as before with the next oil to 
be tested. 

In making comparisons, always test the standard, as well as 
the competing oils, on the same journal and under precisely the 
same conditions. 

It was formerly the custom to continue the trial until the 
temperature of the bearing, as indicated by the thermometer, at- 
tained a certain point, as 120° or 200° F., and to take the number 
of revolutions of the journal or the number of feet traversed, 
up to that point, as a measure of endurance. The real endur- 
ance, however, of the lubricating material bears no definite 
proportion to the range of temperature thus observed. 

Another method is adopted by the boards of U. S. naval 
engineers sometimes appointed to test oils at the navy-yards. 
The quantity of oil required to keep down the temperature of 
journal to a certain figure, as no° or 115 F. (44 to 46 C), 
during a definite period, as one hour, five hours, or twenty-four 
hours, is measured, and the endurance is taken as inversely 
proportional to these amounts. 

The Author considers the endurance of a lubricant to be 
measured by the length of time that it will continue to cover 
and lubricate the journal and prevent abrasion. When an oil 
is placed upon a journal, and there subjected to wear without 
renewal, it gradually assumes a pasty or gummy condition, 
slowly losing its lubricating power, and finally either increases 
friction to an objectionable extent, or oftener becomes so far 
expended as to permit the two rubbing surfaces to come into 
contact. It has been the custom of the author to run until 



262 FRICTION AND LOST WORK. 

this occurs, and then to take the length of the run as a meas- 
ure of the endurance of the oil. 

It is extremely difficult to obtain successive measures of 
similar value even by this method ; but by taking an average 
of several successive trials — or many, if necessary — the true 
measure of the endurance of lubricants can be obtained with 
any desired or necessary accuracy. This method involves 
more risk of injury to the journal than the other, and some- 
times considerable loss of time in bringing the rubbing surfaces 
back into good condition again before going on to make other 
tests. The determination of the real value of the lubricant is 
usually of sufficient importance, however, to justify whatever 
time, trouble, and expense may be thus incurred. 

This machine did such good work as to encourage the Au- 
thor to design one especially fitted for railroad work. 

The journal of this machine is of standard size, 3J inches 
diameter and 7 inches long. The speed is intended to be 
adjusted to velocities varying from that of a twenty-six-inch 
engine-truck wheel at sixty miles an hour down to that of a 
forty-two-inch wheel running fifteen miles an hour. The pres- 
sures are adjustable from a minimum total pressure up to 400 
lbs. per square inch (28 kgs. per sq. cm.), or a load of nearly 
10,000 lbs. (4545 kgs.) on the journal. 

Fig. 42 is a side elevation of the larger machine, with the 
journal and pendulum in section, and Fig. 43 a front elevation. 
It consists of a shaft, AB, which is driven by a cone-pulley, C, 
the whole mounted on a cast-iron stand, D, terminating in a 
forked end at the top, with two bearings, E and F, in which 
the shaft runs. The shaft projects beyond the journal F, and 
the projecting part A is provided with a sleeve or bushing, 
mm, the outside of which forms a journal on which the tests 
of oil are made. A pendulum, AG, is suspended from this 
journal with suitable bearings, aa, which work on the journal 
mm ; the heavy weight, G, attached to the lower end, is now 
omitted. It is evident that the friction on the journal mm 
will have a tendency to move the pendulum in the direction of 
the revolution of the shaft, and that the greater the friction on 
the journal the farther will the pendulum swing. A scale or 



EXPERIMENTS ON FRICTION— TESTING-MACHINES. 263 

dial, HI, is attached to the stand, and the distance the pendu- 
lum swings may be read off on this scale, which thus indicates 
the coefficient of friction of the lubricant on the journal. In 
order to get any desired pressure of the bearings on the jour- 
nal, the pendulum is constructed as follows: A wrought-iron 
pipe, y, which is represented in Fig. 42 by solid black shading, 




Fig. 42. Fig. 43. 

Thurston's "Railroad Machine." 



is screwed into the head K, which embraces the journal and 
holds the bearings aa in their place. In this pipe a loose piece, 
b, is fitted which bears against the under journal-bearing a'. 
Into the lower end of the pipe a piece, cc, is screwed with a 
hole drilled in the centre through which a rod, J, passes, the 
upper end of which is screwed into a cap, d\ between this cap 



264 FRICTION AND LOST WORK. 

and the lower piece, cc, a spiral spring shown in section in Fig. 
42 is placed. 

The upper end of the rod has a cap, e, in which it turns and 
which bears against the piece &, which in turn bears against 
the bearing a'. If the rod is turned with a wrench applied to 
the square head at/, it is obvious that the cap afwill be either 
drawn down on the spiral spring, which will thus be compressed, 
or it will be moved upward, and the spring will thus be released, 
according to the direction in which the rod is turned. If the 
spring is compressed, its lower end will bear against the under 
cap and on the piece cc, by which the pressure will be trans- 
mitted to the pipe./, and thence to the head K, and from that 
on the upper journal-bearing a ; while at the same time the 
upper end of the spring bears against the cap d, which, being 
screwed on the rod f, transmits its pressure upward to the cap 
e, and from that to the loose piece b, and from that to the up- 
per journal-bearing a. It will thus be seen that any desired 
pressure within the limits of the elasticity of the spiral spring 
may be brought upon the journal and bearings by turning the 
rod f. The piece b has a key, /, which passes through it and 
the pipey. This key bears against a nut, o, which is screwed 
on the pipe, its object being to provide a ready means of re- 
lieving the journal of pressure by simply turning the nut o 
when it is desired to do so. An index, t, is attached to the 
spiral spring so as to show the position of the latter. 

A counterbalance is sometimes used to reduce the " mo- 
ment" of the pendulum, when very fine readings are desired. 
This modification necessitates a corresponding change of the 
scale on the arc of the machine. (See Frontispiece.) 

The " brasses" are cast hollow, and when desired a stream 
of water is driven through them to keep the rubbing surfaces 
cool and at uniform temperature. This plan was adopted 
many years ago by Hirn, to secure uniformity and manageabil- 
ity of temperatures. This provision insures great exactness of 
determinations. Provision for lubrication by the oil-bath is 
sometimes advisable for special work. 

The oil is fed to the journal by means of oil-cups, LL, on 
the top of the head K, and a thermometer, T, is attached be- 






EXPERIMENTS ON FRICTION—TESTING-MACHINES. 26$ 



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266 FRICTION AND LOST WORK. 

tween the two cups, and from it the rise in temperature is ob- 
served. A cord, s, is attached to the pendulum in some cases, 
to prevent its being thrown beyond the intended limit. 

The Pratt & Whitney Co., of Hartford, U. S., and Messrs. 
W. H. Bailey & Co., of Salford, G. B., the builders of these 
machines, have slightly modified some of their details, but have 
retained all essential features as in the frontispiece. 

131. Lux's Improvement on Thurston's machine consists 
in the addition of an automatic recording apparatus. The 
pendulum of the machine carries an arm, which raises and de- 
presses a slide at the right, which slide carries a pencil. A cyl- 
inder is mounted behind the pencil-slide, and is connected with 
clockwork, by which it is made to revolve uniformly at any con- 
venient rate. Paper wound on this cylinder is thus made to 
move under the pencil at a constant rate, and the rise and fall 
of the latter is proportional to the swing of the pendulum, and 
varies with the friction at the journal. The paper is suitably 
lined, in such manner that the diagram so made can be conve- 
niently read, the abscissas of the curve measuring the times and 
the vertical scale giving the friction. The pressure is adjusted 
and the temperature readings taken as before. 

The preceding figure exhibits the form of diagram obtained 
during tests of oils in the manner just described. 

132. Illustration of Method, Record, and Report. — 
Results of Trials of an Oil marked X> and its comparison with 
Standard Bleached Winter Sperm and Pure Lard Oils, 

In illustration of the method frequently adopted by the 
Author in making a tolerably complete investigation, we have 
the following: 

These oils were tested on a " lubricant-testing machine" 
of the " 77" style, by the method already described. The 
standard bleached winter sperm and a pure lard oil were tested 
with the X oil on the same bearing and under precisely simi- 
lar conditions. The following are records of data obtained 
during these tests : 



EXPERIMENTS ON FRICTION— TESTING-MACHINES. 267 









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EXPERIMENTS ON FRICTION— TESTING-MACHINES. 2J\ 

From the preceding logs of tests were deduced the follow- 
ing results and conclusions : 

AVERAGE COEFFICIENTS OF FRICTION. 



Lab. 


Name of Oil. 


Pressure per Square Inch. 


No. 


100 


50 


Average. 


90 


W B. Sperm 


0.0037 
0.0168 
0.0062 


0.0050 
O.0206 
O.OIOO 


O.OO435 
0.0187 


X 


93 









The relative values of these oils in reducing friction, taking 
sperm-oil as a standard, and giving it a value of 100, will be 
represented by the quotients obtained by dividing the coeffi- 
cients for sperm by those for each of the other oils, and multi- 
plying by 100. 

The following table gives these quotients: 

RELATIVE POWER OF REDUCING FRICTION. 





Name 


of Oil. 


Pressure per Square Inch. 




100 


50 


Average. 


W. B. Sperm 


IOO. 

22.0 

59-6 


100. 
24.2 

50.0 


IOO.O 


X 


23.2 

53-7 


Lard , 





The speed was about 700 revolutions per minute (244.3 ft-> 
74 m.), giving a speed of rubbing surface corresponding to 
about 35 miles per hour for a 33-inch (79 cm.) wheel in railroad 
service. Dividing the coefficients for the oils by the coefficient 
for sperm and multiplying by 100, we obtain the following 
tabulated figures as the relative amount of power consumed in 
using the respective oils. 

A common standard pressure and speed for such tests is, 
on some roads, 250 lbs. per square inch, and a speed equivalent 
to 15 miles per hour for the axle-journal, at a temperature of 
ioo° F. 






272 



FRICTION AND LOST WORK. 
RELATIVE POWER CONSUMED. 





Name of Oil. 


Pressure per Square Inch. 




IOO 


5° 


Average. 


W. B. Sperm 


IOO.O 
481.O 
167.6 


100.0 

412.0 
200.0 


IOO.O 
429.8 

186.2 


X 







As regards friction, sperm excels, lard stands next, and X 
next. 

From the results of the tests of durability, we find the fol- 
lowing : 

DURABILITY, OR WEARING POWER. 

Revolutions. Ft. travelled. 

W. B. Sperm 27,870 9,726.6 

X (average) 26,380 9,206.6 

Lard 24,500 8,550.5 

Taking bleached winter-sperm oil as a standard, and assum- 
ing its value to be 100, the values of the oils as regards dura- 
bility will be represented by 100 times the quotient obtained 
by dividing the number of revolutions or feet travelled of each 
oil by the feet run by sperm. We thus obtain the following: 

RELATIVE DURABILITY. 

W. B. Sperm 100 . o 

X 94.6 

Lard 87.9 

The figures in this last table are measures of the lengths of 
time that equal quantities of each oil would run, so that the 
greater the figures of this table the more valuable the oil. 

The value of an oil may be taken as greater in proportion as 
the figures in the above table are greater, and as the figures in 
the table headed " Relative Power of Reducing Friction" are 
greater, so that combining the results given in both tables, the 
relative values of the oils, sperm-oil being the standard and 
taken at 100, may be represented by one one-hundredth the 
product obtained by multiplying the figures in the last column 
of the table headed " Relative Durability" by those in the last 
column of the table headed " Relative Power of Reducing 
Friction." The following are therefore the relative values. 



EXPERIMENTS ON FRICTION— TESTING-MACHINES. 273 



RELATIVE VALUES OF THE OILS. 
W R Soerm 


. . 100. 


x 


.. 21.9 


Lard 


.. 47.2 



Second Test. 

A second test consisted in cutting a square hole in the lower 
box and packing it with waste saturated with the oil to be 
tested. The oil to be tested was spread on the journal and a 
pressure of 100 lbs. per square inch (43 kgs. per sq. cm.) was- 
applied ; the machine was then started and allowed to run 
until the friction had increased to double the least amount 
shown at any time during the test. Both the X and the lard 
oils were tested by this method. In each case 743 milli- 
grammes weight of waste was used as packing. The waste 
was in each case thoroughly saturated with the oil and weighed 
before and after the test. In the case of X, the waste absorbed 
4.806 grms. and contained 2.229 g rms - at the end of the test, 
so that the oil consumed was 2.577 grms. In the case of the 
lard, 4 grms. were also absorbed by the waste; 7.265 grms. 
remained ; so that the useful consumption was 2.735 g r ms. X 
ran 266,226 ft. = 54.2 miles per gramme consumed, with an 
average coefficient of friction of 0.0318, and lard-oil ran 
182,528.7 ft. = 34.5 miles per gramme consumed, with an 
average coefficient of friction of 0.0244, the former excelling 
the latter about sixty per cent. 

Third Test. 
A third test was made upon the " R. R. Standard Machine," 
and the following are the coefficients of friction obtained : 



AVERAGE COEFFICIENTS OF FRICTION. 



Oil. 


Pressure per Square Inch and Total. 


150, 
2629 


300, 
5250 


Average. 


W. B. Sperm 


O.008 
O.024 
O.009 


O.OO46 

O.OI5 

0.0059 


0.0063 


X ... 

Lard 


O.OI95 
O.OO75 





CHAPTER VII. 

FRICTION OF LUBRICATED SURFACES— LAWS AND MODIFYING 

CONDITIONS. 

133- Variations of Friction of Lubricated Surfaces oc- 
cur, as has been already stated, with every change of physical 
condition of either the bearing and journal surfaces, or of 
the lubricant applied to them.* A rough pair of surfaces ex- 
hibits great resistance to relative motion, while this friction is 
constantly reduced as they become smoother with wear ; but 
under some conditions the smoothness and the nicety of fit 
may be made too perfect, and the friction then increases again. 
An oil which works well, and gives a comparatively low coef- 
ficient under low pressures, may prove an inferior lubricant un- 
der heavy loads, and the same unguent may be a good, a bad, 
or an indifferent lubricant according to the temperature or the 
speed of the rubbing surface to which it is applied. It is even 
sometimes found to be the fact that, with some lubricants, and 
especially with light mineral oils, the total frictional resistance 
may be reduced, while nevertheless the bearing may show in- 
creased wear, the increase of resistance due to the exceedingly 
slow wear being compensated by the decrease in fluid resist- 
ance. 

The conditions which produce most serious differences in 
ordinary work are the nature of the unguent, the pressure, and 
the temperature. Velocity of rubbing determines a limit be- 
yond which the intensity of pressure cannot be carried without 
danger of heating ; but the effect of its variation upon the 

* Friction and Lubrication. New York, 1879. 



FRICTION OF LUBRICATED SURFACES. 



275 



coefficient of friction is usually less considerable than is that of 
either of the other conditions specified. 

The lubricating value of oils is even affected by moisture. 
It affects mineral oils very little, the moisture slightly increas- 
ing their resistance in the bearing. They have little tendency 
to absorb moisture from the atmosphere. Fatty oils are some- 
what hygroscopic, and are quite sensibly affected by a trace of 
moisture. 

Exposure to air produces a tendency in organic lubricants 
to acidify or to become resinous, the non-drying oils exhibiting 
the one and the drying-oils the other method of change. The 
purer the oil, as a rule, the less is the liability to change. 
Hirn, experimenting on the oils named below, found that some 
were rather better lubricants at the period of incipient rancid- 
ity than when fresh. Cocoa-nut oil was 7 per cent, and rape 
seed 3 per cent, better, while with other oils less difference is 
observed. 

Working the oils for a week together, using an oil-bath, 
Hirn finds sperm-oil to alter least of all, very slowly increasing 
in resistance ; neat's-foot next, then olive and rape-seed ; while 
cocoa-nut oil depreciates most rapidly, and at a rapidly acceler- 
ated rate. 

The time required to exhibit an acid reaction was as below : 



Oils. Time, hours. 
Sperm, first quality 36 

" second quality 36-38 

Lard 24 

Neat's-foot 30 

Olive, limpid 24-30 



Oils. Time, hours. 

Cocoa-nut 4 

Poppy 5 

Rape seed, refined 12 

" crude 24 



Sperm-oil was found to be the best lubricant in all these 
experiments. 

The method of supply should be carefully looked to, and a 
very free "feed," with a system of collection and reapplication 
of the oil leaving the bearing, will be found to give by far the 
greatest economy of power and cost. Experiments made for 
the Institution of Mechanical Engineers, in which oiling by a 
pad as in railway work, by a siphon lubricator or oil-cup, and 
by a bath, which keeps the surfaces flooded with oil, gave the 



276 



FRICTION AND LOST WORK. 



COEFFICIENTS OF FRICTION. 

\ Journal of Cast Iron ; Bearing ; Bronze ; Velocity, 750 feet (230 m.) per minute 
Temperature, 70 F. (21 ° C). Intermittent feed through oil-hole.] 



Name. 



Group I. 



Natural Summer Sperm 

" Winter Sperm 

Bleached " " 

" Summer Whale 

Natural " " 

" Winter Whale 

Bleached " " 

Winter Lard Oil 

Extra Neat's-foot Oil 

Tallow Oil 

Refined Seal Oil 

Bleached Winter Elephant Oil. 

Group II. 

Olive Oil 

Cotton-seed Salad Oil 

Palm Oil 

Rape-seed Oil 

Elaine Oil 

Linseed Oil * 

Pea-nut Oil 

Refined Cotton-seed Oil 

Rosin Oil 

Cocoa-nut Oil 

Cold-Pressed Castor Oil 

Group III. 

Labrador Cod Oil 

Tanner's Cod Oil 

Menhaden Oil 



Group IV.$ 
Mineral Sperm Oil. 



Deod. White Lubricating 

Bleached Deod. Lubricating — 
Unbleached Deod. Lubricating 

Kerosene* 

Crude Lubricating. 



Pressures: 
Lbs. per Square Inch and per Square Cm. 



0.56 



32 
2.24 



Avge. 



1720 
2505 
1920 
1866 
1986 
3296 
1979 
2386 
2242 
1840 
1585 
1928 



1668 
2156 
2826 
1817 
2597 
1598 
1910 

2I2S 

2765 
1750 

237s 



• 2475 
.2776 
.2530 



• 1875 

• 1537 

•1833 

■ 2550 

• 2330 

272 



Paraffine 1 . 2607 



Min. 



Group 
Natural Winter Sperm. 
Bleached " " 

Natural " Whale. 
Bleached " " 

Winter Lard ... 

Extra Neat's-foot 



Group II. 



Olive Oil 

Refined Rape-seed (Yellow 1 * 

Winter-pressed Cotton-seed (White). 
Winter-pressed Cotton-seed (White). 



Group III. 



Menhaden Oil. 



J 33° 
1500 
1583 
1333 
1500 

1833 
1333 
1666 
1500 
1500 
1333 
1333 



1333 
1577 
1666 

1333 

2000 

1333 
1500 
1666 
2650 
1333 
1916 



1500 
2166 
1660 



1333 
1500 

1333 
1500 
2165 
1 100 
2000 



Avge 



1627 
1410 
,1600 
1383 
1482 
1902 
1916 
1575 
1621 
1460 
1378 
1650 



•1575 
•1757 
.2041 
.1567 
.1842 
.1215 
.1688 
.1401 
• 2452 
.1066 
.1380 



.1666 
.1238 



1604 
1583 
2333 
2067 
1729 

1453 
1777 



Min. 



.1083 
.1000 
,1330 
,09166 
,0916 
,1250 
13^3 
1 166 
1000 
1000 
1083 
1083 



1000 
1250 
1250 
1250 
1500 
0833 
!333 
1249 
1500 
0916 
1125 



.1250 
.1500 



.1416 
.1500 
.1500 
.1500 
.1416 
.1000 
• 1333 



Avge 



. 102 

.0958 

.1172 

.1109 

.1316 

.0925 

.1086 

.1405 

.1166 

•°935 

. 1 190 

.0862 



1444 
1116 
1187 
1277 

J 347 

10052 

1166 

1170 

1062 

1026 



.1016 
.0970 
. 1000 



.1277 
.1250 
•1275 
.1250 
.1777 
•1343 



Min. 



.0833 
,0875 
0916 
0874 
1086 
0750 
1000 
1000 
0916 
0750 
0916 
0791 



.1000 
.1083 
0584 
.0833 
.0833 
.0750 
.0792 
.1000 
•0833 
.o 79 it 
.0708 



0666 
0833 
0917 



.0791 
.1125 
.1166 
.1250 
.1250 
.1500 
.1125 



48 
3.36 



Avge 



.1180 

.0813 

.09907 

.0881 

.0951 

.1444 

•0993 
.1005 
.1138 
.1166 
.0986 
.0766 



0930 
0996 
1013 
1063 
1305 
0962 

0833 
1 100 
1028 
0794 
0944 



.0805 
.0880 
.1220 



0944 
1277 
1222 
1555 
1770 
1500 
2222 



Min. 







Second Series of 


Tests 




.2072 

• 1755 

• 2369 

• 1747 

• 1959 
.1746 


• 1333 
.1166 
.2166 

• 1333 

•1583 

• 1500 


.1661 
.1678 
.1250 
.1483 
.1770 
1254 


.1291 
.1291 
.1000 

•1133 
.1250 
.1000 


.1302 
.1083 
.1000 

• 1333 
.1095 
.1198 


.0958 
.0958 
.0750 
.0833 
.0666 
.0791 


•1155 
.0811 
.0777 
.0986 
.0758 
•1159 


.1839 
.1716 

.1259 
• 1557 


• 1333 
.1666 
.1166 

• 1333 


•1175 
•1435 
.0981 
.1006 


.0916 
.1166 
.0833 
•0833 


.0902 
. 1000 
.0983 
.0895 


.0750 
.0833 
.0666 
.0750 


•1344 
.0822 
.0861 
.0758 


■ 1637 


• 1333 


.1685 


.1083 


.0982 


.0625 


.0963 



• 105a 

.0750 
.0944 
.0777 

.0722 
.1000 

.0705 
.0750 

• 1055 
.0844 
.0750 
.0611 



OS5S 

0694 

0666 



0609 

0550 

0800 

0844 

061 1 
0722 



.0661 
•0833 
. 1000 



0944 
1277 
1222 
1444 
1770 
1500 
2222 



.0750 
.0666 
.0666 
.0666 
.1000 



.0611 
•o555 
.0750 
.0722 



* Not a lubricant. 

t Values somewhat uncertain. 

% All mineral oils here described are of uncertain composition. 



FRICTION OF LUBRICATED SURFACES. 



277 



following figures, showing an enormous advantage in the use 
of the last method : 

METHODS OF OILING (RAPE-SEED OIL). 

Velocity of rubbing, 157 feet (46 m.) per minute. 





Actual Load. 


Coefficient 
of Friction. 


Comparative 
Friction. 




Kilogs. per 
sq. cm. 


lbs. per 
sq. in. 


Oil Bath 


18.5 
17-7 
19 1 


263 
252 
272 


O.OOI39 
O.OO980 
O.009OO 


I 


Siphon Lubricator. . . . 
Pad under Journal. ... 


7.06 
6.48 



The lowest of these values of the coefficient are below any 
reached by the Author, or, up to their date, probably, ever 
recorded. 

134. Commercial Oils, under moderate pressures, vary 
greatly in their power of reducing friction. The table of 
values (p. 276) obtained by the Author by experiment, using 
the testing-machine devised by him, exhibits the effect of varia- 
tion of pressure in changing these values, as well as the differ- 
ences in oils, all of which were supposed to be pure. These 
values may probably be assumed as correct, and applicable in 
the ordinary work of the designing engineer. 

In this case the journal was of cast-iron, running in gun- 
bronze bearings, and was in very good, but not in the very 
best possible, condition. As will be seen, much better figures 
may be obtained. The oils were here supplied intermittently, 
but frequently, in the usual manner, and the results may be as- 
sumed to be substantially the same as with continuous feed. 
The first series were not all fresh ; the second set were fresh and 
pure. 

To show how these figures were obtained, the results are 
given below in detail and in the usual tabular form, as obtained 
by the Author by trial of a good sample of winter-bleached 
sperm-oil. It should be remembered that precise agreement 
between two tests of even the same oil, under nominally the 
same conditions, never can occur except by a rare accident, as 
the oil itself is never precisely alike throughout — sperm-oil, for 
example, varying in quality with its purity and age, and with 



278 



FRICTION AND LOST WORK. 



the age, sex, health, and habits of the fish from which it was 
taken, etc., and the conditions of the journal and the other 
circumstances affecting the trial can rarely if ever be dupli- 
cated with absolute precision. These differences are not usu- 
ally of practical importance, but the precaution is always taken 
to compare each oil tested with a standard pure sperm, care- 
fully preserved, to be tested immediately before or immedi- 
ately after the test of the oil to be examined. The quantity 
of oil here adopted was 332 milligrammes — enough to flood 
the journal at one application. 



DETAILS OF TEST. 
Best Winter-bleached Sperm Oil. 

First Trial. 

Amount used upon the journal 332 milligrammes. 

Speed of rubbing surface , 736 ft. (224 m.) per minute. 

Pressure per square inch and per cm 8 lbs. (0.56 kgs.). 

Total pressure 30 lbs. (13 . 6 kgs.). 





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Fahr. 








Fahr. 






Start. 
























min. 


75 







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160 


3-5 




79 


190 


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5-5 




119 


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139 


235 


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159 


240 


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121 


218 


6.5 




141 


235 


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161 


240 


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123 


220 


6-5 




143 


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163 


240 


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125 


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165 


243 


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127 


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M7 


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167 


243 


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129 


230 


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149 


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169 


243 


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131 


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151 


238 


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171 


244 


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133 


232 


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153 


240 


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173 


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135 


234 


6.5 




155 


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7 




175 


256 


7 


Mean 


137 


234 


7 




157 


240 


7 




177 


260 


7 


0.1875 



FRICTION OF LUBRICATED SURFACES. 



279 



Second Trial. 

Amount used upon the journal 332 milligrammes. 

Speed of rubbing surface 736 ft. (224 m.) per minute. 

Pressure per square inch 16 lbs. 

Total pressure 60 lbs. 



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avge 
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Third Trial. 

Amount used upon the journal * 332 milligrammes. 

Speed of rubbing surface 736 ft. (224 m.) per minute. 

Pressure per square inch 32 lbs. 

Total pressure 120 lbs. 















u 
















u 






























G 






3 ^ 








3 














c 

















5 c 




























a 










a 
















4* O «j 

8 03 


£ 


u 



C ) 


£ 


&°3 
a 03 

u 


0.3 


£°3 


H 


(j O ai 
Ol, rt 

a m 




sa°t; 




H 










H 








H 






At 


























Start. 


80 









5 


210 


11.5) 


0.096 

mini- 


11 


295 


15 
to 




1 


95 


21 






7 


235 


mum.' 


12* 


320 


25 


av'ge 


3 


170 


15 






9 


260 












0.1317 



Fourth Trial. 

Amount used upon the journal 332 milligrammes. 

Speed of rubbing surface 736 ft. (224 m.) per minute. 

Pressure per square inch 48 lbs. 

Total pressure 180 lbs. 



















































V 


a co 


a 


C G 

.2 


a> 


a » 


B 


.2 


u* 


3 CO 


c* 


c a 
.2 


a 


u « 


"J3 c° 


se°.H 


a 


fe*S 2 

a 2 


'£ to 


i£ °.| 


a 


a, 2 




Sfi^.u 




a 03 


& 


h 




a 03 


fe 


fc, 

u 




a 03 


fe 


( o h 




H 








H 








H 






At 
























Start. 


80 







3 


180 


" 1 


0.0833 
mini- 


7 


285 


30 
to 




1 


100 


20 




5 


235 


16 | 


mum. 


8 
9 


320 

345 


40 


av'ge 
0.1194 






280 



FRICTION AND IOST WORK. 



135. The Relative Standing of Oils, such as are found 
in the market, as determined by their power of reducing fric- 
tion, and economizing work and energy, when used on ma- 
chinery in which the pressures are low, is readily determined 
by the study of the preceding table. The columns of mini- 
mum values of the coefficient of friction may be taken to rep- 
resent the values of the oils there named when lubrication is 
continuous and free; and these values are those to be selected 
for the purposes of such a comparison. 

Comparing the oils tested at any one pressure, it is seen 
at once that they differ greatly in their power of reducing 
friction at whichever pressure they are compared. All give 
lower coefficients as the pressure rises ; but the differences are 
great at all pressures. The following table exhibits the rela- 
tive standing of the oils named at the several pressures re- 
corded : 



RELATIVE STANDING OF LUBRICANTS. 

First Series. 





Pressures. 






[Lbs. per sq. in. and kgs. per sq. cm.] 




Order. 










8 


16 




32 


48 




0.56 


1.12 




2.24 


3-36 


z 


Crude Mineral Lubri- 


Natural Whale 


and 


Palm. 


Pea-nut. 




cating. 


Cocoa-nut. 








2 


Nat. Summer Sperm. 


Nat. W. Sperm. 
Ex. Neat's-foot. 




Labrador Cod. 


Olive. 














Tallow. 












Olive. 












Menhaden. 












Crude Lub. 








3 


B. S. Whale. 


N. S. Sperm. 




C. P. Castor. 


B. W. Elephant. 




B. W. Whale. 


Ref . Seal. 






Cocoa-nut. 




Refined Seal. 


B. W. Elephant. 










B. W. Elephant. 












Olive. 












Rape-seed. 












Cocoa-nut. 












Mineral Sperm. 












Bl. Deod. Min. Lub. 










.4., 


N. W. Sperm. 
N. S. Whale. 


C P. Castor. 




N. W. Whale. 


Labrador Cod. 








Tallow. 






Ex. Neat's-foot. 












Tallow. 












Pea-nut. 












Lab. Cod. 












Deod. W. Min. Lub. 












Unbl. W. Min. Lub. 











FRICTION OF LUBRICATED SURFACES. 28 1 

RELATIVE STANDING OF LUBRICANTS— Continued. 





Pressures. 
[Lbs. per sq. in. and kgs. per sq. cm.] 




8 
0.56 


16 
1. 12 


32 
2.24 


48 
3-36 




Cotton-seed. 
B. W. Sperm. 

Menhaden. 

W. Lard. 

Palm. 

Ref. Cotton-seed. 

N. W. Whale. 

B. W. Whale. 

N. S. Whale. 

Ex. Neat's-foot. 

Tallow. 

Pea-nut. 

Lab. Cod. 

Deod. W. Min. Lub. 

Unbl. W. Min. Lub. 

Cotton-seed. 

B. W. Sperm. 
Menhaden. 

W. Lard. 

Palm. 

Ref. Cotton-seed. 

N. W. Whale. 

C. P. Castor. 

Elaine. 
Paraffine. 
Tanner's Cod. 
Rosin. 


W. Lard. 

Ref. Cotton-seed. 

N. W. Whale. 
Cotton-seed. 
Palm. 
Rape-seed. 
Lab. Cod. 
B. W. Sperm. 

B. W. Whale. 

Pea-nut. 

Paraffine. 

Mineral Sperm. 

Elaine. 

Rosin. 

Tanner's Cod. 

Deod. W. Min. Lub. 

Bl. W. Min. Lub. 

Unbl. W. Min. Lub. 


Cocoa-nut. 
Mineral Sperm. 
N. S. Sperm. 
Rape-seed. 
Elaine. 
Cocoa-nut. 
Tanner's Cod. 
B. W. Sperm. 
Ex. Neat's-foot. 
Ref. Seal. 

Menhaden. 

B. W. Whale. 

Winter Lard. 

Olive. 

Ref. Cotton-seed. 

Cotton-seed. 

N. S. Whale. 

N. W. Sperm. 
W. Lard. 
Ref. Seal. 
Menhaden. 

B. W. Whale. 

W. Lard. 

Olive. 

Ref. Cotton-seed. 

Cotton-seed. 

N. S. Whale. 

Deod. W. Min. 

Paraffine. 

Bl. Deod. Min. 

Unbl. Deod. Min. 
Crude Min. 


Palm. 


6 


Cotton-seed. 
B. W. Whale. 


8 


N. S. Whale. 


9 


Rape-seed. 
C. P. Castor. 
N. W. Sperm. 
W. Lard. 
Ref. Seal. 


ii 


Tanner's Cod. 
Tallow. 


*3 

^4 




Rosin. 

B. W. Sperm. 
Mineral Sperm. 
N. W. Whale. 






Tanner's Cod. 
Tallow. 


16 




Rosin. 

B. W. Sperm. 
Mineral Sperm. 
N. W. Whale. 
Menhaden. 
N. S. Sperm. 


*7 

18 
















Bl. Deod. Min. 










Deod. Min. 
Unbl. Min. 
Crude Min. 
Paraffine. 



2%2 



FRICTION AND LOST WORK. 



RELATIVE STANDING OF LUBRICANTS, 

Second Series. 



Order. 




Pressures. 
[Lbs. per sq. in. and kgs. per sq. cm.] 






8 

0.56 


16 
1. 12 


32 

2.24 s 


48 
3.36 


i 


W. P. Cotton-seed. 
B. W. Whale. 
Olive. 
Menhaden. 
Ex. Neat's-foot. 

W. Lard. 

Ref. Rape-seed. 

N. W. Whale. 


W. P. Cotton-seed. 

N. W. Whale. 
Ex. Neat's-foot. 
Menhaden. 

B. W. Whale. 
Ref. Rape-seed. 

W. Lard. 

N. W. Sperm. 
B. W. Sperm. 


Menhaden. 

W. Lard. 

W.P Cotton-seed. 

N. W. Whale. 

Olive. 

W.P. Cotton-seed. 

Ex. Neat's-foot. 

B. W. Whale. 

Ref. Rape-seed. 

N. W. Sperm. 

B. W. Sperm. 


Ref. Rape-seed. 
Olive. 




N. W. Sperm. 
B. W. Whale. 
W. Lard. 
W.P.Cotton-seed, 






N. W. Sperm. 
Menhaden. 
Ex. Neat's-foot. 


6 











Studying these tables, a number of interesting facts are 
revealed. It is seen that when under moderate pressures 
whale-oil is better than sperm, while as pressures rise the 
sperm gains in value, finally excelling whale. This difference 
will be found still more marked under very heavy pressures. 
The mineral oils fall at the end of the list under pressures ex- 
ceeding the lowest here given, although standing well under 
the minimum. As will be seen elsewhere, these light oils 
make excellent spindle-oils, and are good lubricants for such 
low pressures as are met with in the working of textiles. 
They vary enormously in quality, however, and the Author has 
met with refined petroleums which fully equal sperm under 
the heaviest pressures. This has since been observed by other 
investigators. Olive-oil stands well under all pressures here 
reported on, as do the other vegetable oils generally. Castor- 
oil is too viscous for general use, however. Tallow and neat's- 
foot oils are better at the lower than at the higher of these 
pressures ; the reverse is the case with palm and cotton-seed 
oils. 

It is to be remembered that the order of standing just deter- 
mined is liable to be changed by a change of velocity or of 
temperature, and by alteration of pressure outside the range 
here given. 

It was found by Mr. Woodbury that the best neat's-foot oil, 



FRICTION OF LUBRICATED SURFACES. 



283 



used as a spindle-oil, absorbed 3.2 times as much power as the 
best refined light petroleums. The mixed oils are sometimes 
best for heavy machinery; unmixed refined petroleum of low- 
density is probably best for light machinery. The following 
are the figures obtained by test at low pressure, moderate 
speed, and standard temperature, the conditions being as nearly 
as possible those met with in spinning-frames. 

COEFFICIENTS OF FRICTION FOR SPINDLE-OILS. 



Order of 
Value. 



Oil. 



Refined Petroleums, Heavy Spindle. 



Light Spindle 

Extra Machinery. 



Lard 

Bleached Winter Sperm, 



Unbleached Winter Sperm. 
Bleached Winter Sperm.. . 

Seal Oil 

Neat's-foot 



Coefficient of 

Friction at ioo 

Degrees, F. 



O.H87 
O.1233 
O.1208 
O.II13 
O.II32 
O.0756 
O.2181 
O.IO67 
O.I2I7 
0.1 170 

O.O956 

0.1 147 
0.1141 
0.1608 
0.2427 



These "thin" spindle-oils cannot be used at high pressures 
and low speeds ; heavy viscous oils only remain between the 
surfaces, unless carried in by rapid motion of journal. 

The experiments of Mr. Beauchamp Tower, made at the 
request of a committee of the British Institution of Mechanical 
Engineers,* give several oils the following relative standing, 
as averages for loads from 100 to 310 lbs. per square inch (7 to 
22 kgs. per sq. cm.) : 

Comparison of Oils — Relative Friction. 

Oil. Grease as Standard. Sperm as Standard. 

Sperm Oil 0.48 1.00 

Rape-seed Oil 0.51 1.06 

Mineral Oil 0.62 1.29 

Lard Oil 0.65 1-35 

Olive Oil 0.65 1.35 

Mineral Grease i.oo 2.17 



* Proceedings, 1883. 






284 



FRICTION AND LOST WORK. 



These figures are supposed by their author to represent 
closely the resistance, the body or viscosity, and the weight- 
carrying power of these unguents, the latter being considered 
proportional to the viscosity of the oil. It was found that the 
resistance of rape-seed oil, taken as an example, was one eighth 
as great when the journal was worked in an oil-bath as when 
oiled with a siphon cup, or by a pad, the coefficients being 
0.0014, 0.0098, and 0.0090, respectively. 

The best lubricants, as a rule, have the lowest weight-carry- 
ing power. The Author has used sperm-oil under pressures 
fully equal to, and even sometimes exceeding, those attainable 
with other oils — a result, however, which is not accordant with 
the experience of some other investigators. 

136. The Relative Endurance of Oils tested on the 
journal used by the Author in making determinations of the 
coefficients of friction has been ascertained for a number of 
the more common lubricants. The difficulties met with in 
attempts to determine with even approximate accuracy the 
wearing power of lubricating materials have already been re- 
ferred to ; but only experience can enable any one to secure 
reliable data. 

Testing a number of the oils of commerce* for durability, 
on a cast-iron journal, there were used 32 milligrammes at 
each application, and the time noted required to run the jour- 
nal dry, with the following result : 

OILS OF COMMERCE, AVERAGE ENDURANCE. 



Pressure per 


Running Time. 


Rise of 
Temp., b. 


Average co- 
efficient, ./• 


Heat 
coefficient, 


Square Inch. 


Ave. a. 


Min. 


Max. 


?,=;? 


8 lbs. 

16 " 

32 " 
48 " 


82 
29 
IO 

8 


17 
9 
2 


411 
97 
*9 
13 


167° F. 

212 
228 

228 


0.20 
O.16 
O.I2 
O.IO 


0.50 
0.14 
0.05 
0.04 



The " heat coefficient" is valuable as exhibiting the relative 
increase of temperature per minute during the trial. Its value 

* This collection iacluded many oils of little value as lubricants. 



FRICTION OF LUBRICATED SURFACES. 



285 



is sometimes — usually wrongly, although in some cases nearly 
correctly — taken as a measure of endurance. 

Several well-known oils ran thus — the speed being 750 ft. 
(230 m.) per minute : 

ENDURANCE, ETC., OF LUBRICANTS ON CAST-IRON. 



Name. 



Summer Sperm. . 

Lard 

Olive 

Cotton-seed 

<« i< 
Cod 

< « 
Crude mineral (?) 



Lbs. 

per 

sq. in. 



16 
48 

8 

16 
4S 

8 

16 
4 S 

8 

16 
48 

8 
16 
48 

8 

16 
43 



Running- 
Time. 



Ill min. 

29 " 

9 " 

165 " 

33 " 

7 " 

83 " 

41 " 
14 " 

107 " 

45 " 

12 " 

40 " 

14 " 

9 " 

129 " 

97 " 

5 " 



Rise of 
Temperature. 



230^ 

225 

195 
270 

215 
265 

170 

245 
240 

185 
275 
310 
200 

175 
220 

I05 
2S5 
270 



F. 



Coefficient, 
/■ 



O.13 
O. IO 
O.08 



O.I3 

IO 

06 

16 

12 

07 
O.I5 
O.I2 
O.O7 
O.IO 

0.10 

O.IO 



Heat 
Coefficient, C. 



O.48 
O.I2 
O.04 
O.61 
O.15 
O.02 
0.4S 
O.16 
O.05 

0.57 
O.16 
0.03 
0.20 

O.08 
O.04 
1.22 

0.34 
0.02 



Comparing a mixture of plumbago and grease with sperm- 
oil, the former was found to have a lower coefficient, to heat 
up less rapidly, and to endure several times as long. It was 
also indicated that plumbago in very fine flakes was better 
than in an impalpable powder. 

Testing sperm and lard oils for durability, on a small steel 
journal, gave : 

ENDURANCE OF SPERM AND LARD OILS. 
Durability of one 8-milligramme drop: Feet Run. 



Pressure per sq. in. 
" " " cm 

Sperm 

Lard 



7204 
6797 



7685 
7139 



250 
17-5 



7675 
7090 



7521 
700S 



286 FRICTION AND LOST WORK. 

Others of the commercial oils found in the market and largely- 
purchased by consumers, who have no means of testing them, 
endure but for a very small fraction of the time and the dis- 
tance travelled with sperm and lard, and the Author has rarely 
if ever found an oil which equals sperm in this quality. 

The " Railroad Machine" has given the following for sperm 
and lard oils, using a much larger quantity than was taken 
above : 

300 lbs. 500 lbs. 

Sperm, raw (ft.) 19,800 13,500 

Lard, " " 10,557 7.515 

The coefficients being at the same time, 

Sperm 0.0046 0.0033 

Lard 0.0059 0.0044 

The journal was in this case of very soft steel, of standard 
size, and was driven at a speed corresponding to 30 miles an 
hour. 

In the attempt to make use of such determinations of the 
endurance of lubricants in daily practice, the investigator 
meets with a serious difficulty which has, however, no relation 
to the character of the material used. It is an important fact, 
and one which should be constantly borne in mind, that the 
maximum wearing power of a lubricant, as it is here denned 
and determined, has no necessarily definite relation to the 
quantity which will be actually used, or even required, when 
working under other conditions. 

Usually, the same amount will be used, whether it be of 
great or of little wearing power, the amount being usually 
determined by the method of feeding, rather than by its in- 
trinsic character. Other things being equal, the more viscous 
lubricant will feed more slowly, and will therefore be appa- 
rently of higher wearing power than the more fluid lubricant ; 
a grease will last longer than an oil ; the method of applying 
the lubricant to the journal will determine whether it is 
economically or wastefully used. These are vastly more im- 
portant facts than they are generally supposed. Regular 



FRICTIOISf OF LUBRICATED SURFACES. 28/ 

trains on railroads have been known to use nine times as 
much grease as an experimental train on which the most 
rigid economy was exercised.* 

It thus becomes evident that the proper method of proce- 
dure is to first determine the value of the lubricant by a series 
of careful tests at the pressures, velocities, and temperatures, 
and with the kind of rubbing surfaces proposed to be used, 
then to find, and to adopt, that method of feeding which will 
insure maximum economy. As a rule, however, determina- 
tions of endurance are of comparatively little value in every- 
day practice, because their use is rarely, and seldom can be, 
regulated by their endurance ; the same amount would gene- 
rally be used, and the same quantity wasted, whether the 
wearing quality be high or low. The real value of a lubricant 
is therefore generally measured by its power of reducing fric- 
tion. 

The following are the details of a trial reported at the 
Brooklyn Navy Yard, in which a less certain but less trouble- 
some method was adopted : 

The oil was measured by dropping. The same quantity, 
■five (5) drops, was used in all the tests. 

When a seeming discrepancy appeared, or doubt arose re- 
garding any result, the experiment was repeated until satis- 
faction was obtained. The driving power came from the 
Navy-Yard engine, and the speed of the testing-machine varied 
with the work done by the engine. Owing to this cause it 
was not claimed that the results were absolutely correct. The 
average speed was however taken, which so nearly approxi- 
mates uniformity, that the data may be considered correct for 
all practical purposes of comparison. Two series of tests were 
made, one of three-minutes runs, and another of one minute 
each. 

* Railroad Gazette, Sept. 20, 1878. 



288 FRICTION AND LOST WORK. 

ENDURANCE OF SPERM AND LARD OILS. 

One-Minute Runs. 



Oils. 


Revolutions. 


Increase of 

heat in units 

of degrees 

Fahrenheit. 


Coefficient, c. 


Comparative 

efficiency, 

sperm being 

100. 




a. 


6. 


a 

6 = C - 


h. 


Sperm. 


1812 
1790 

1883 
I8IO 


43-5 
46 
50 
50 


41.6 

38.8 

37-6 
36.2 


IOO 


Prime Lard 


93-2 

90.5 
87.02 


Lard No. i 


Lard No. 2 



Three-Minute Runs. 



Oils. 


Total 
Revolutions. 


Per 

Minute. 


Increase of 
heat in units 
of degrees 
Fahrenheit. 


Coefficient, 


Comparative 

efficiency, 

sperm being 

100. 




d. 


a'. 


e. 


*-'■ 


*-. 




5506 

5741 
5428 
5500 


I835-3 
I9I3-6 
1807 
1833 


82 
90 
90 
96 


67.I 
63.8 
60.3 

57-3 


IOO 


Prime Lard 

Lard No. 1 


95-1 
89.8 

85.4 







Columns b and e give the increase of heat in degrees 
(Fahrenheit) of the journal, starting from a nearly constant 
temperature of 78 or 8o°. The unit of comparison is the 
number of revolutions obtained for each degree of increase in 
temperature, and is obtained, in the minute runs, by dividing- 
column a by column b which gives the coefficient column c T 

(7- == c\, and in three-minutes runs by dividing column d by e y 

giving the coefficient in column/, (—=/). 

Columns h and h r compare the efficiency on the basis of 
sperm being 100. 

It need hardly be repeated here, that the ratio of heat 
developed to revolutions made or distance traversed has no 
necessary and definite relation to the real power of endurance 
of the oil. 

The real value of a lubricant to the user is a somewhat 
difficult quantity to determine, since it really depends, not 



FRICTION OF LUBRICATED SURFACES. 



289 



upon the relative friction-reducing power and endurance, as 
usually assumed, but upon the value of the power saved by its 
use. This value varies in every case, and is affected by every 
variation of working conditions. 

So far as the value of these oils is determined by durability, 
it is seen that sperm excels lard oil very greatly ; it has already 
been seen that it also excels in power of reducing friction 
under the conditions of test here met with. 

The first of the tables in this article shows the time of 
endurance of the oils to be dependent upon the pressure under 
which they are worked, and to decrease in a higher ratio than 
those pressures increase, even within the moderate range there 
given. The second table shows lard-oil to excel sperm, olive, 
cotton-seed, and the mineral oils, at the lowest pressure; while 
it becomes, next to the mineral oils, the lowest at the highest 
pressure, under which load olive-oil stands first and cotton-seed 
second. The change to a fine steel journal, running in bronze, 
and under much higher pressures, makes sperm-oil far the 
better when compared with lard, which result is confirmed by 
the navy experiments, which make sperm ten per cent better 
than lard. 

The following illustrates the value of a crude well-oil from 
the Shoshone Wells, Wyoming, as compared with sperm taken 
as a standard. 

This oil is intensely black, and the coloring matter is in- 
separable. On distillation there was obtained : Naphtha, 0.63 ; 
0.47 kerosene having 159 F. flash-test; 0.32 of a neutral and 
light-colored lubricating oil ; and 0.12 dry coke. The oil as it 
flows has a gravity of 20 B. Its flash-test is 294 and fire-test 
322 F. (146 and 161 C). Cold-test 16 below zero (- 27 
C). The results of tests by the Author were : 





FRICTION. 

Coefficient of Friction. 




Name of Oil. 


Pressure. 


50 lbs. 
3-5 k&s. 


200 lbs. 
14 kgs. 


300 lbs. 
21 kgs. 


Sperm 


O.0034 
0.0077 


. 005 1 
0.0085 


0.0057 
0.0071 


Black Oil 





290 



FRICTION AND LOST WORK. 



Assuming sperm to be 100, the following table gives the 
relative value of the oils as reducers of friction : 

Value in Per Cent. 



Name of Oil. 



Sperm. . . 
Black Oil 
Lard 



Pressure. 



50 lbs. 
3-5 kgs. 



I .OO 
O.44 



200 lbs. 
14 kgs. 



300 lbs. 
21 kgs. 



I. OO 
O.60 
0.75 



I.OO 

O.80 
0.75 



ENDURANCE. 


Name of Oil. 


Number of Revolutions. 


Feet Travelled. 




First Trial. 


Second Trial. 


First Trial. 


Second Trial. 


Sperm 


21,300 
11,700 


24,400 
12,000 


7,434 
4,083 


8,516 

4,188 


Black Oil 



Sperm taken at 100, the following represents the relative 
wearing power : 

Value Per Cent. 



Name of Oil. 


First Trial. 


Second Trial. 


Averages. 


Sperm 


1.00 

0.55 


1.00 
O.49 


1.00 


Black Oil 


O.52 
O.52 


Lard 







GUMMING. 



Value. 
IO 



Sperm 

Black Oil 6.25 

Lard 5 • 5© 

The following records of tests made by the Author exhibit 
both the methods and the results, as derived by trial of reputed 
pure oils. The first table illustrates the test of good lard-oil, 
determining its friction-reducing power and its endurance at 
ordinary temperatures, and its heating action under a common 
moderately heavy pressure. Its best work is seen to give a 
minimum value o(f= 0.0173, or about one and three quarters 
per cent, the average for the test rising to one fourth of one 



FRICTION OF LUBRICATED SURFACES. 



29I 



per cent with " free feed," the oil passing to the journal by the 
usual system of feeding through the cap of the " brass." In 
the endurance test the distance rubbed over at the rate of 400 
feet per minute, using 8 m. g. of oil, on a journal four inches in 
circumference and about if inches long, was nearly 6000 feet. 

Comparing these figures with those for sperm-oil, sum- 
marized in the next record, it is seen that the latter, a reputed 
sperm-oil, but certainly not of the highest quality, exhibits a 
somewhat higher coefficient, but fifty per cent, more endurance. 

STANDARD LARD OIL. 



Laboratory No., . Original Mark, " L ". Source— The Manufacturer. Composition- 
Pure Lard Oil. Investigation— To determine Friction and Endurance. Coefficient of Fric- 
ReadingonArc 



tion = 



Total Pressure 



Friction. 



Endurance. 



No. of Test , 

Pressure on journal, lbs. per sq. inch 

Total pressure on journal, lbs , 

Amount of oil used on journal, m. g. 

Average coefficient of friction 

Minimum " " 

No. of revolutions 

No. of feet travelled by rubbing surface 
Elevation of temperature, max 



I. 
100 

300 
Free feed 



o 0245 0.023 
0.0176 I 0.0173 
Per minute. 
1200 
400 
77° F. 



400 
66° 



III. 

100 
300 



o-53i 
0.046 



IV. 

100 



0.0516 



Total. 



0.040 



17,567 
5,856 
190 



17,062 
5,687 



Time, 
Minutes. 



Revolu- 
tions. 



Tem- I Read- 
pera- sing on 
ture, F.| Arc. 



Coeffi- 
cient of 
Friction 



Test I. — Friction. 







15 
7.8 


6,000 


150° 


12,000 


164° 


6.1 


18,000 


171° 


6.1 


24,000 


173° 


5-8 


30,000 


175° 


5-5 


36,000 


177 


5-3 
Av'ge 



Test II. — Friction. 





IIO° 


14 


6,000 
12,000 


157° 
169° 


7-5 
6.0 


18,000 


173° 


5-6 


24,000 


!74° 


5-5 


30,000 
36,000 


!74 
176 


5-2 
5-2 

Av'ge 



Test III.— Endurance. 

I 82 I 16.5 

"o° 17.5 



min. 

0.0176 

0.0245 



min. 

0.0173 

0.023 



Time, 

Minutes. 


Revolu- 
tions. 


4 
6 






8 








13 





Tem- 
pera- 
ture, F. 



Read- 
ing on 
Arc. 



i95^ 

220° 



250" 
268° 



272 

Redistributed oil 



22.0 
23.0 
19. o 
17-5 
22.0 



Coeffi- 
cient 
of Fric- 
tion. 



220° 


14.0 


240 


16.O 


250 


20.0 




Av'ge 



Test IV. — Endurance. 



IOO 


14-5 


130° 


12.0 


160 


I2 -5 


185° 


16.0 


213° 


15-5 


245° 


22.5 



Redistributed o 
220 



245 
2 68 c 



14. 





14. 


5 


18 




Av 


'ge 



min. 
0.046 



.0631 



min. 
0.040 



0.0516 



292 



FRICTION AND LOST WORK. 
SPERM OIL 



Laboratory No., 



Original Mark, 



Source, . Composition— Reputed Sperm 



Oil. Investigation— To determine general value. Coefficient of Friction = ^ ead '" g ° n Arc - 

Total Pressure 



No. of Test 

Pressure on journal, lbs. per sq. inch 

Total pressure on journal, lbs 

Amount of oil used on journal, m. g 

Average coefficient of friction 

Minimum " " 

No. of revolutions 

No. of feet travelled by rubbing surface 
Elevation of temperature, max Fahr 



Friction. 



I. 

100 



300 
Free feed 



0.0272 
0.0203 

Per minute. 
1200 
400 
106 



0.0242 
0.0193 



1200 
400 
8 3 ° 



Endurance. 



III. 
100 
300 



IV. 

100 
300 



Total. 



22,320 

9,440 

175° 



The same lard-oil tested as a "cylinder-oil" gives in one 
case, here presented, the varying coefficient of friction which 
gradually decreases, as the temperature rises, from /"= 0.032 
at ioo° F. to f— 0.003, or one tenth the first value, at 350 , 
and which becomes /= 0.008 at 200 when rising and 
f=. 0.022 at the same temperature when descending the scale 
of temperature. Repeating the test, the same general results 
are observed. 

The elevation of temperature observed during the test, 
where, as in these examples, no attempt is made to control it, 
will be seen to follow very closely the frictional resistance. It 
therefore is evidently a gauge of lubricating quality which may 
serve to assist the judgment in rating oils by comparison when 
no more exact method is available. 

STANDARD LARD OIL. 



Laboratory No., . Original Mark, " L". Source— The Manufacturer. Composition- 
Pure Lard Oil. Investigation- To determine value as a " Cylinder Oil." Coefficient of Fric- 
Reading on Arc 
Total Pressure 



Hon 



No. of Test 

Pressure on journal, lbs. per sq. inch 

Total pressure on journal, lbs 

Amount of oil used on journal, m. g 

Average coefficient of friction 

Minimum " " 

No. of revolutions per minute 

No. of feet travelled by rubbing surface. 
Range of temperature, max. Fahr 



I.— Rise. 


II.-Fall. 


III.— Rise 


100 


100 


100 


300 


300 
Free feed 


300 
in all tests. 


0.098 


0.0163 


0.0141 


0.003 


0.0043 


0.003 


1200 


1200 


1200 


400 


400 


400 


250 


132 


250 



IV.— Fall 

100 
300 

0.0953 
0.004 

1200 
400 

150° 



FRICTION OF LUBRICATED SURFACES. 



293 



Time. 
Minutes. 



Revolu- 
tions. 



Tem- 


Read- 


pera- 


ing on 


ture. 


Arc. 



Coeffi- 
cient of 
Friction 



Test I.— Rise. 



I0O° 

110° 


9-5 
8.0 


120° 


7.0 


I 3 0° 


6.0 


I4O 


4-9 


150° 
l6o° 


4-3 
3-8 


I7O 

180 


3-3 
3-° 


190 


2.8 


200° 


2-5 


2IO° 


2.2 


220° 


2.1 


230° 


2.0 


240° 
250 
26o° 


1.9 
1.8 

1.6 


27O 
28o° 


i-5 
1.4 


29O 


i-3 


3 00° 
3IO 


1.2 


32O 


1.0 


33°° 


1 .0 


340° 


1.0 


350° 


A ', 9 

Avge 



Test II.— Fall. 



34°° 


i-3 


33°° 


2.0 


320 


2-3 


3io° 


3-5 


300 


4.8 


290 


5-3 


280 


5-5 


270 


5-6 


260 


6.0 


250 


6.2 



min. 
0.003 
0.090 



min. 
0.0043 



Time. 

Minutes. 



Revolu- 
tions. 



Tem- 

pera- 



240^ 
230 

220 
2IO° 

208 



Read- 



ing on 
Arc. 



Coeffi- 
cient of 
Fricti'n 



6.0 
6.2 
6.2 
6.3 
6.5 
Av'gei 0.0163 



Test III.— Rise. 



IOO° 


J 4 


5 


IIO° 


11 


■> 


120° 


9 


8 


130° 


8 


7 


I4O 


7 


9 


I 5 2° 

160 


7 
6 


2 

5 


170 
180 


5 
4 


5 
3 


i 9 o° 


4 


1 


200° 


3 


7 


220° 







2 4 0° 
260° 


2 


3 




28o° 


1 


7 


3OO ° 


1 


3 


320° 


1 


1 


340° 


1 





35"° 



A\ 


9 



Test IV.— Fall. 



340 
320° 


; 


2 

6 


300 
280 


2 


9 
6 


260 


3 





240 

220° 


3 

3 


6 
8 


200° 

180 


4 

4 

A^ 


3 
9 
r'ge 



min. 
0.003 
0.0141 



min. 
0.004 



SAMPLE OF GRAPHITE OIL. 



Laboratory No., . Original Mark, . Source, . Composition— Heavy Mineral Oil. 

Plumbago in Suspension. Investigation — To determine real value of the Oil. Coefficient of 
Reading on Arc 
Total Pressure 



Friction 



No. of Test 

Pressure on journal, lbs. per sq. inch 

Total pressure on journal, lbs 

Amount of oil used on journal, m. g 

Average coefficient of friction 

Minimum " " , 

No. of revolutions , 

No. of feet travelled by rubbing surface 
Range of temperature, max. Fahr 



Friction. 



A. 
100 

300 



too 
300 



Free feed. 

0.029 I 0.0312 

0.018 I 0.0206 

Per minute. 



1200 
400 
107 



1200 
400 
103 



Enduranci 



A. 

100 

300 

8 

0.0626 

0.0416 

Total 
17,000 
5,666 
i 94 ° 



B. 

100 

300 

8 

0.063 

0.04 

15,210 

5,070 



I 



294 



FRICTION AND 10 ST WORK. 



MINERAL CYLINDER OIL AND GRAPHITE. 

Laboratory No., . Original Mark, . Source, . Composition— Heavy Petroleum 



and Graphite in proportions not given. Investigation- 
Reading on Arc 
Total Pressure 



-To determine value as Cylinder Oil. 



Coefficient of Friction 



No. of Test 

Pressure on journal, lbs. per sq. inch 

Total pressure on journal, lbs 

Amount of oil used on journal, m. g 

Average coefficient of friction 

Minimum " " at 350 , 340 , 330 , 320 

No. of revolutions per minute 

No. of feet travelled by rubbing surface per minute. 
Range of temperature, max. Fahr 



I.— Rise. 


II.— Fall. 


III.— Rise 


100 


100 


100 


300 

. 0208 

0.0043 

1200 


300 300 

Free feed in all. 

0.0099 0.0221 

0.0050 0043 

1200 1200 


1200 

260 


1200 
145° 


1200 
250 



V.— Fall 
100 
300 

0.00997 
0.0050 

1200 

1200 

iso- 



Similar tests of a mineral oil containing graphite in sus- 
pension, as above given, show that the latter may be so mixed 
as to give an excellent result, while retaining the peculiar 
qualities of the plumbago-oils. The endurance above recorded 
*is about that of lard-oil; while the best values of f are those 
of the best mineral and sperm oils under similar conditions. 

The mixing of mineral and animal oils yields, in some cases 
at least, unexpected results. Thus a mineral oil, rich in paraf- 
fine, being compared with lard-oil by the Author, gave the 
following, under 100 lbs. pressure per square inch : 

f. Values. 

Mineral Oil 0.0150 100 

Lard Oil 0.0160 0.94 

Mineral, 95 ; Lard, 5 0.0120 127 

" 90; " 10 0.0140 107 

In endurance these oils stand : 

Mineral Oil 100 

Lard Oil 120 

Mineral, 95; Lard, 5 125 

" 90; " 10 160 

Combining the two values, for a total relative standing, 

gives : 

Mineral Oil too 

Lard Oil 113 

Mineral, 95 ; Lard, 5 160 

" 90; " 10 171 

The introduction of graphite does not always increase 
either the endurance of an oil or its friction-reducing power, 
but probably always gives increased safety against " cutting" 



FRICTIOX OF LUBRICATED SURFACES. 



295 



or abrasion, either as an effect of higher pressure or excessive 
temperature. It is often difficult to secure a permanent mix- 
ture. 

A mixed oil, mainly heavy petroleum, was compared by 
the Author with lard, pure, but of ordinary quality only, on 
the same journal and under as nearly as possible identical con- 
ditions, with the results given in the succeeding tables. The 
mineral oil, tested by variation of temperature, congealed at 
io° F. (- 12 . 2 C), melted at 24 F. (-^C), flashed at 
480 F. (249 C), and took fire at 540° F. (292 C). It was 
perfectly neutral, exhibiting no acid reaction even when 
heated to the point of decomposition. The minimum values 
of f, as given in these tables, may be taken as the real gauge 
of the value of the oil ; since the best conditions should 
usually be maintained, as a matter of economy, whatever the 
quantity of oil demanded to give them. This oil excelled lard 
oil 10 per cent, in its friction-reducing power, and had con- 
siderably more than double the endurance of the latter ; as a 
cylinder-oil it was vastly superior, also, at high temperatures, 
such as are met with in steam-cylinders. 

CYLINDER OIL. 

Laboratory No., X. Original Mark, L. Source — Manufacturer. Composition— Heavy 
Petroleum and and Animal Oil. Investigation— To determine Friction and Endurance. Coef- 
Reading on Arc, 



ficient of Friction = 



Total Pressure 



No. of test 

Pressure on journal, lbs. per sq. inch. 

Total pressure on journal, lbs 

Amount of oil used on journal, m. g. . 

Average coefficient of friction 

Minimum coefficient of friction 



No. of revolutions 

No. of feet travelled by rubbing surface. 
Range of temperature', max. Fahr 



300 



300 



Free feed. 

0.0218 I 0.0218 

0.0178 I 0.0178 

Per minute. 



,200 

400 

6o« 



1,200 
400 



64" 



3 

100 

300 

8 

0.0405 

0.0318 

Total 
27.200 
9,060 
174' 



4 
100 



0.0455 
0.0328 

30,120 

10,040 

165° 



CYLINDER OIL (Same). 

Composition— Heavy Petroleum and Animal Oil. Investigation- 

r« i- j ^m r a: ■ c n- • ■ Reading on Arc. 

Cvhnder Oil. Coefficient of Friction = — — 

Total Pressure 



-To determine value as a 



inch. 



No. of Test 

Pressure on journal, lbs. per sq 

Total pressure on journal, lbs 

Amount of oil used on journal, m. g 

Average coefficient of friction 

Minimum coefficient of friction 

No. of revolutions per minute 

No. of feet travelled by rubbing surface, per minute 
Elevation of temperature, max. Fahr 



I. Rise. 


II. Fall. 


III. Rise 


100 


100 


100 


300 


300 
Free feed i 


300 
n all cases. 


0.00718 


0.00715 


0.012 


0.0035 


0.0038 


0.0035 


1,200 


1,200 


1.200 


400 
260 


400 
170 


400 
26b 



300 

0.008 
0.0036 
1,200 
400 

170° 



296 



FRICTION AND LOST WORK. 



137. Pressure modifies Friction to a very important 
extent, as is seen plainly in the tables already given of coeffi- 
cients of friction of the commercial oils. The general effect 
is to reduce the coefficient of friction rapidly, as pressures in- 
crease in intensity, until a minimum is reached, passing which 
the coefficient still more rapidly increases, until abrasion and 
" cutting" take place, causing frequently serious injury of the 
machine and great waste of power. 

The next three tables exhibit this fact quite as strikingly 
as the preceding. It presents the results of the experiments 
of the Author at pressures rising to 1000 lbs. per sq. inch (70 
kgs. on the sq. cm.), and upon both a cast-iron journal, as in 
the first set, and upon a steel journal in more perfect condi- 
tion. 

On examination of the tables given in Article 134, we are 
at once impressed with the immense difference which occurs 
with variation of pressure. It is seen that, at a pressure of 48 
lbs. per square inch (3.36 kgs. per sq. cm.), the values are 
not far from those quoted by accepted earlier authorities, but 
at the lower pressures, where the resistance is due more to 
viscosity than to true friction, the value of the coefficient of 
friction immensely exceeds those familiar values. It is instruc- 
tive to compare these figures with those obtained at high 
pressures, with which object we give the table below. Tested 
on a fine steel journal, with free lubrication, the figures be- 
come but a fraction of those already given. Sperm, lard, and 
West Virginia oil, thus tested by the Author, give : 



COEFFICIENT OF FRICTION ON FINE STEEL JOURNALS. 



Name. 


Pressure • i Lbs - P er sc l uare in ch. 
Pressure . -j Kjlos per squafe cm 


4 
0.56 


10 
0.9 


25 

i-7S 


150 
10.5 


200 
14 


250 
17-5 


275 
12.3 


300 

21 


500 

35-o 




0.12 


0.08 


0.041 
0.056 


0.0090 
0.0136 
0.0120 


0.0096 
0.0127 
0.0095 


0.0086 

O.OIIO 

0.0081 


0.0091 
0.0090 
0,0100 


O.OO46 
O.OO59 


0.0033 
0.0044 























FRICTIOX OF LUBRICATED SURFACES. 



297 



2 


3 


4 


5 


0.14 


0.21 


0.23 


0-35 


0.27 


0.22 


0.1S 


0.17 



The experiments of Mr. Woodbury :; give the method of 
variation of the figures for still lower pressures, thus : 

•n ( Lbs. per sq. inch. . 1 

Pressure : -J r ^ 

( " " cm... 0.07 

Values of f. .. . 0.3S 

These values of the coefficient of friction of motion were 
obtained on new surfaces at a temperature of ioo° F. (38 C), 
and at a velocity of 600 feet per minute. The surfaces were 
probably not quite equal to those just described, or the lubri- 
cant may not have been equally good ; the figures are consid- 
erably higher. 

Here it is seen that the figures are as widely different from 
accepted values at high pressures as at low, but that the differ- 
ence is upon the other side. At those pressures, therefore, 
which are most used in heavy machinery the resistance of 
friction is vastly less than we have been led to suppose, while 
the friction of very light machinery is very much greater. The 
fact that the journals here used were of steel, instead of iron 
in the first case, does not modify these conclusions. Steel, 
cast-iron, and wrought-iron all give very nearly the same 
figures up to their limits of pressure, when well worn. 

The next table exhibits the results of experiment up to 
still higher pressures, and with other journals and bearings: 



COEFFICIENTS OF FRICTION, OF MOTION, AND OF REST, 
(a.)— Cast Iron Journal and Steel Boxes. 



a 

u 


"0 
c 

& 

on 
u 

8. 


B. W. Sperm. 


West Virginia. 


Lard. 




u 
V 

0. 


stf 




"S-- 


tJ^ 


s 


■g.' 


«*> s 


OE* 


Temperature in all cases 


Ma 


£^ 


8 2 


tx 


^ 


OX br 


£ S 


less than 115 Fahrenheit. Ve- 


3 
en 


u 

3 


U. 3 

.r 


la 




O.S 
5S 


« 


2 D. 


ISOF 

Minu 
tartin 


11 


locity of rubbing, 150 feet per 
minute. 


1 


t/3 

a 

PL. 


<%. 


Cri 

< 


<c/5 


<§. 


< 


*j 2 
<<75 




*J 


W. B. Sperm. Lard. 
Ratio of — = .75 for 500, .77 


3.5 


50 


.013 


.07 


•°3 


.0213 


.11 


.025 


.02 1 .07 


.01 


a 

b 
Ratio of — = .888 for 1000, .90 


7.0 


100 


.008 


•135 


.025 


.015 


•135 


.025 


.0137 .11 


.0225 


17-5 


250 


.005 


•14 


.04 


.009 


.14 


.026 


.0035 .11 


.016 


a 


35-o 


500 


.004 


•IS 


■°3 


.00525 


•15 


.018 


.00525 .10 


.016 




52-5 


75° 


.0043 


.185 


■03 


.005 


.185 


.0147 


.0066 1 .12 


.02 




70.0 


1,000 


.009 


.18 


•03 


.010 


.18 


.017 


.0125 1 .12 


.019 








(3.)— Steel Jou 


rnals and Brass B 


oxes. 






35-o 


500 


.0025I 




.004 [ 






70.0 


1,000 


.008 

1 




.009 







* Proc. N. E. Cotton Man. Assoc, 1S80, p. 61. 



298 FRICTION AND LOST WORK. 

Studying this table, we see that with these oils the coeffi- 
cient in these cases rapidly diminishes with increase of pres- 
sure, until a pressure of over 500 lbs. per square inch (35 kgs. 
per sq. cm.) is attained ; the coefficient, after passing a pres- 
sure of probably 600 to 800 lbs. per square inch (42 to 56 kgs. 
per sq. cm.), increases, and at 1000 lbs. (703 kgs.) becomes 
about equal to that obtained at 100 lbs. (7 kgs. per sq. cm.). 
It will be remembered that 500 or 600 lbs. pressure (35 to 42 
kgs. per sq. cm.) is usually considered to be a limit not to be 
exceeded in general practice in machine construction. 

Nevertheless, it is not uncommon to find as high pressures 
as 1000 or even 2000 lbs. (703 to 1406 kgs. per sq. cm.) in the 
crank-pins of steam-engines. In such cases, however, the pins 
are almost invariably of steel, and the journals of good bronze 
— conditions which are less seldom met with elsewhere. 
There is also in this case, as wherever a " reciprocating force" 
acts to move a piece, a condition which permits higher pres- 
sures to be successfully worked than can be reached else- 
where ; the alternate application and relief of pressure occur- 
ring between journal and bearing at each change of direction of 
the driving-force causes a release, at such times, which permits 
the oil to find its way between the rubbing surfaces, and its 
expulsion is not then fully effected before the succeeding 
relief of pressure again permits its renewal. A somewhat 
similar action is consequent upon the rise and fall of a loco- 
motive or of a railway-car on its springs as it rapidly traverses 
even a smooth track. Where this relief cannot take place, the 
limit of pressure is earlier met. In exceptional cases, of very 
slow motion, or of quickly relieved pressure, as in cotton- 
presses, the limit is higher, sometimes six or seven times the 
higher figure, above. 

138. The Law of Variation of Friction with pressure may 
be approximately determined from the above. Referring to 
the last table, it is seen that between 100 and 750 lbs. the 
value of the coefficient may be obtained approximately by the 

expression f = , in which a is a constant quantity and P 

is the pressure in pounds per square inch ; for sperm-oil 



FRICTION OF LUBRICATED SURFACES. 



2 99 



a — 0.080, for crude heavy mineral oil a — 0.150, and for lard- 
oil a = 0.125.* For a wider range the rather less handy ex- 
pression, 

f= — 

may be adopted, making a from 0.25 to 0.40. No such expres- 
sions can be accepted as general ; they are purely artificial, and 
only applicable under the conditions of observation upon which 
they are based. It will presently be seen that the law is modi- 
fied by temperature and speed. 

The following data were given by trials of two excellent 
kinds of grease, and of sperm-oil, compared with them as 
standard. 



COEFFICIENTS OF FRICTION OF GREASES. 

Steel Journals ; Bronze Bearings. Velocity, 300 ft. 



Lubricant. 


Pressure- -1 k bs< per S( *- in - 
r-ressure. y Kgg per §q cm 


Average. 


100 
7 


200 
14 


300 
21 


400 
28 


500 

35 


Sperm Oil 

Grease, No. I. . . 
" No. 2. . . 


O.OI4I 

O.O249 
O.OI88 


O . OO63 
O.OI46 
O.OI98 


O . OO49 
O.OI25 
O.OI60 


O.OO42 
O.OIO5 
O.OI46 


O.OO39 
O.OII4 
O.OI75 


O.O067 
O.OI40 
O.OI7 



Their relative average values in reducing friction stand, 
therefore: Sperm, ioo; No. I, 44.8; No. 2, 37.7: which figures 
would also represent their relative money values if estimated 
on that basis simply. 

The method of variation with pressure already noted is 
here again illustrated, although the mathematical expression 
has a different set of constants, and the variation at this speed 
is more nearly as the inverse ratio of the cube-root of the 
pressure. 

It was also concluded by Hirn, as a deduction from his 
experiments on lubricants, that the resistance varies as the 
square root of the pressure. 

* These facts and deductions were published originally in a paper prepared in 
the spring of the year 1878, and read at the St. Louis meeting of the American 
Association for the Advancement of Science. 



30O FRICTION AND LOST WORK. 

In the table is presented a set of values of the coefficients 
of friction, of motion, and of rest which are both new and im- 
portant. In the columns headed "At 150 feet per minute" 
are given the coefficients of friction at the several pressures 
as obtained when the rubbing surfaces are in motion at that 
relative velocity. These are the common and most usually 
required figures. We have in the other columns, however, 
values which are seen at a glance to be immensely greater, and 
of which the values vary by an entirely different law. 

The first set, " At starting," are the well-understood coeffi- 
cients of friction of rest, varying with the pressure and with the 
nature of the unguent from 0.07 to 0.18. These values had 
never been determined before in this manner, and possess 
great importance, not simply intrinsically, but also as throwing 
some light upon the effect of motion upon the efficacy of lub- 
rication. It is seen that they increase with the pressure, instead 
of diminishing, as do the coefficients of friction of motion, and 
that at the highest pressures their values become from ten to 
forty times the corresponding values of the latter. 

In the effort required to move heavy machinery, vastly 
greater force is demanded to overcome friction at the instant 
of starting than after motion has once commenced. 

The method of variation of the coefficient for rest is seen, 
by reference to the table, to be such that their numerical values 
may be approximately estimated, for the cases here considered 
by the formula, 

/' = a' >V7; 

in which a' = 0.02 for sperm and heavy mineral oil, and 
a' = 0.015 for lard-oil. 

The figures in the columns headed " At instant of stopping" 
were given while the machine was rapidly coming to a stop, 
after the driving-belt had been shifted to the loose pulley. 
They are, as would be expected, intermediate in value between 
the other figures, and have apparently no practical importance. 
They may be taken as constant at all pressures. Even these 
figures are probably higher than those sometimes reached with 
old journals which have been kept in good order many months 



FRICTION OF LUBRICATED SURFACES. 3OI 

or years, and which have worn to that remarkable mirror-like 
smoothness which is familiar to every experienced mechanic. 
Values, on the "railroad machine," have been, for sperm, and 
even for lard, as low as one fourth of one per cent., at pressures 
of less than 500 lbs. per square inch ; while cylinder lubri- 
cants, applied to bearings heated to the temperature of steam 
at 100 lbs. pressure, have given coefficients as low as one 
ninth of one per cent., and flooded journals with the oil-bath 
have even done better than this. 

Later experiments, to be described, show that, as has been 
already indicated (§ 135), the most perfect lubrication attainable 
sometimes gives values of the cofficient varying nearly inversely 
as the pressure, and making the total frictional resistance 
nearly independent of pressure. Intermediate conditions give 
intermediate methods of variation. 

The general conclusion that the coefficient of friction 
decreases with increasing pressure must evidently be qualified 
by the undoubted proposition that, with any given condition 
of the rubbing surfaces, and with all other conditions un- 
changed, there must always be ultimately reached a point at 
which, with increasing pressures, the limit of bearing power is 
attained or approached, and the friction must exhibit a change 
of law, the coefficient increasing, beyond that limit, as the 
intensity of pressure is augmented. The safe limit has been 
given in § 127, when considering size of journals. 

The method of variation of the friction of lubricated sur- 
faces with variation of pressure is also well shown by Fig. 45, 
representing results given by Mr. Waite. The experiments 
illustrated were made at a temperature of ioo° F. (48° C). 
Here, paraffine oil (light spindle-oil) is seen to offer increasing 
resistance with increasing pressure, at a nearly uniform rate, 
but with a decreasing coefficient, until a pressure of 22 lbs. 
per square inch (1.5 kgs. per sq. cm.) is reached, when the 
coefficient becomes nearly constant, the total resistance increas- 
ing very nearly as the pressure. 

Lard-oil exhibits a similar " critical point," at about 40 
lbs. (2.8 kgs.), and sperm at about 72 lbs. per square inch 
(5 kgs. per sq. cm.) ; while neats-foot oil has no such point 



302 



FRICTION AND LOST WORK. 



within the limits of the diagram. In each case, the decrease 
of the coefficient is shown by the parabolic form of the curve, 



































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which would become a straight line were the coefficient con- 
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cient to increase with pressure. 



FRICTION OF LUBRICATED SURFACES. 



303 



Fig. 46 exhibits the same change, as observed by Wood- 
bury, at low pressures and at various temperatures, the range 
falling below 5 lbs. per square inch (0.35 kgs. per sq. cm.), 
and between yo° and 120 F. (21 and 49 C), the speed 
remaining constant. 

Experiments made for the Author at various times, * on 
the machine designed by him and already described, have been 
collated and are graphically represented in Fig. 47, in which the 
curves exhibit the method of variation of friction with pres- 



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COEFFICIENT OF FRICTION 



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Fig. 46. — Friction and Pressure. 

sure under ordinary conditions of lubrication, at various speeds 
of rubbing, from 30 to 1200 feet (9 to 366 m.) per minute. 

It is found that at the lowest speed the effect of variation 
of pressure is very similar to that at higher speeds at tempera- 
tures not differing far from those common in machinery, but 
that the effect is very different, and somewhat peculiar, at 
higher temperatures. At the lower temperatures the coeffi- 
cient decreases with great rapidity at first, passes a minimum 
at usually not far from 100 lbs. per square inch (7 kgs. per sq. 
cm.), and again rises, although but slowly, as the pressure is in- 
creased to 200 lbs. (14 kgs. per sq. cm.), the change occurring 
very regularly. 

The minimum here observed is carried to higher pressures 
as the speed of journal and the efficiency of lubrication are in- 



* Friction and Lubrication, 1879, etc. 



304 



FRICTION AND LOST WORK. 



COEFFICIENTS OF FRICTION. 
.015 .020 .025 .030 .035" .040 .045 .05C 



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Fig. 47.-— Pressure vs. Friction. 



FRICTION OF LUBRICATED SURFACES. 305 

creased, and has been reached in experiments made by the 
Author, in some cases, at very much higher figures than those 
here given ; the best figures attained being f=- 0.0025 at vari- 
ous times, with the ordinary system of oiling, and at pressures 
ranging, with sperm-oil, from 100 to $00 lbs. per square inch 
(7 to 35 kgs. per sq. cm.), according to state of the journal and 
conditions of working. Oil-bath lubrication is found, at high 
speeds of journal, to carry the minimum beyond the working 
range of pressure, and to bring the coefficient down to a mini- 
mum of not far from one tenth of 1 per cent. 

139. Velocity of Rubbing is an important element in de- 
termining the loss of work and energy by friction, where the 
surfaces are lubricated. 

The experiments of Poiree and Bochet * show that between 
velocities of 900 and 3600 feet (270 and 1080 metres) per min- 
ute the coefficient of friction of brakes and of wheels skidding 
on the rails diminished very greatly — approximately from 0.2 
to 0.13. The surfaces were not lubricated. 

In the year 1858, Mons. H. Bochet presented his paper on 
this subject to the French Academy of Sciences, in which he 
states that he had found the coefficient of friction between 
surfaces of iron to be variable, diminishing as velocity increased. 

M. Bochet proposed what was equivalent to the following 
formula: 

__ a -f- bcv 

in which /is the coefficient of friction, and a, b, and c are con- 
stants ; v is the velocity of sliding in metres (or the velocity 
in feet divided by 3.28) per second. The values of these con- 
stants were (no lubrication) : 

a — 0.3 to 0.2 for dry and 0.14 for moist surfaces ; 
b = 0.03 for wheels and 0.07 for skids on rails ; 
c = undetermined, but taken as negligable. 

* Mem. de la Soc. des Ing. Civ., 1852, p. no, etc. Comptes Rendus, xlvi. 
(1858), p. 802, and li. (i860) p. 974. 



306 



FRICTION AND LOST WORK. 



Prof. Kimball * determined the following table of coefficients 
for pine sliding on pine (dry), and deduced the conclusions: 

(i) At a given inclination, the friction decreases with in- 
creasing velocity, at first rapidly, then more slowly. 

(2) At the same velocity, the friction is greater the greater 
the angle of the sliding plane. 

(3) The value of the coefficient tends to become constant. 

(4) The value of this constant seemed to be the same for 
all experiments. 



COEFFICIENTS OF FRICTION. 

Pine on Pine. 

Pressure, if- lbs. per square inch (0.12 kg. per sq. cm.). 



Velocity per 


Second. 




Values of 


Coefficient. 




ft. 


m. 


1 


2 


3 


4 


4 


I 


0.260 


O.273 






10 


3 


0.252 


O.261 


O.270 


0.280 


20 


6 


0.243 


O.248 


O.264 


0.260 


30 


9 


0.237 


O.242 


O.256 


0.250 


40 


12 


0.233 


O.236 


O.240 


0.2J.2 


SO 


15 


0.230 


O.232 


O.235 


O 236 


60 


18 


0.228 


O.23O 


O.231 


O.232 


80 


24 


0.224 


O.226 


O.226 


0.225 


IOO 


31 


0.222 


O.223 


0.22I 


0.222 


120 


37 




0.220 


O.217 





At pressures double and five times the above, the law still 
held. 

Later experiments f gave the following : 

Pine on Pine. 
Pressure, 4 lbs. per square inch (0.28 kgs. per sq. cm.). 



Velocity, 
inches per minute. 

5 
11 

75 
100 



Coefficient 
of Friction. 

0.I9 
0.2I 
O.24 
O.25 



* American Journal of Science, 1876. 
flbid. 



FRICTION OF LUBRICATED SURFACES. 



307 



Velocity in 
inches per min. 

O.79 

1.58 

3-94 

9.98 

29.14 



Leather on Pine. 
Pressure, 4 lbs. per Square Inch. 



Coefficient 
of Friction. 

O.41 

0.43 
0.45 
O.46 

0.475 



Velocity in 
inches per min. 


Coefficient 
of Friction 


72.50 


0.22 


I57.50 


O.27 


226.80 


0.33 


300 . OO 


O.36 


466 . 00 


O.38 



Leather Belts on Cast-iron Pulleys. 



Velocity in inches 
per minute. 

0.37 

O.52 

I.I 

2-3 

4.4 

15-4 

34-1 

80.3 

228.8 



18 

92 

660 

1 190 

1980 
2669 



T 2 lbs. T, lbs. 


c. 


30 13 


0.41 


30 I2-J- 


0.44 


30 Hi 


0.48 


30 lo£ 


0.53 


30 9i 


0.58 


30 6£ 


0.78 


30 5i 


0.86 


30 4i 


0.96 


30 4i 


1.50 


■Repeated at Higher Speeds. 






0.82 




0.93 




1. 00 




0.96 




0.82 




0.69 



The values of C are relative, and are not the absolute 
values of the coefficients of friction. With a wrought-iron 
shaft, turning in cast-iron bearings, well oiled, and a load of 66% 
lbs. per square inch (4.7 kgs. per sq. cm.), at velocities of rub- 
bing of 72, 272, 605, and 1320 inches per minute, the frictional 
resistance varied as 1, 0.60, 0.40, and 0.29; at the very low 
speeds of 0.007, 0.027, 0.060, and 0.132 inches per minute, the 
relative resistances were as 0.37, 0.51, 0.73, and 1.00. 

Professors Jenkin and Ewing,* experimenting at still lower 
velocities — 0.0002 to 0.01 foot (0.00006 to 0.0003 m -)> an d again 



* Proceedings of Royal Society, 1876-77. 



308 FRICTION AND LOST WORK. 

up to 0.6 foot (0.18 m.), per second — with various metals and 
without lubrication, found a similar law to prevail. 

In Professor Jenkin's experiments at extremely low veloci- 
ties, he has shown that, where there is a very great difference 
between the two coefficients of friction of rest and motion, the 
coefficient of friction decreases gradually as the velocity in- 
creases, between speeds of 0.012 and 0.6 foot (0.0036 and 0.183 
metre) per minute. In cases where there is little or no dif- 
ference between the coefficients of rest and motion, no differ- 
ence was found at the various velocities between which he 
experimented. His experiments were made with a small steel 
spindle of 0.1 inch (2 J millimetres) diameter, carried in rectan- 
gular V notches, the pressure being constant, and due to the 
weight (86 lbs. = 39 kgs.) of a disk carried by the spindle and 
revolving with it. The more recent experiments of M. Marcel 
Deprez, with the disk of a dynamo-electric machine, started at 
very high velocity and slowly retarded by its own friction of 
journals and bearings, show a constantly decreasing resistance 
from 0.025 at 550, to 0.005 at J 4S revolutions per minute, the 
friction remaining constant between 145 and 120 revolutions at 
0.005, and then rapidly increasing as the disk comes to rest. 
The average value of the coefficient was 0.0013. The weight 
of disk and shaft was nearly two tons, and the journal was 2 
inches (0.06 m.) in diameter. 

These experiments show that there exists a continuity of 
values between the gradually varying coefficients for decreas- 
ing velocities and those obtained for statical friction. 

The experiments reported by Kimball,* on journals run- 
ning with lubrication under pressure of 15 to 25 lbs. per 
square inch (1 to 1.75 kgs. per sq. cm.), gave the following: 

Velocity in m. per minute 0.3 

Velocity in ft. per minute 1 

Coefficients o. 150 

Velocity in m. per minute 6 

Velocity in ft. per minute 20 

Coefficients 0.058 



* American Journal of Science, March, 1878, p. 194. 



I 


1.5 


2.1 


3 


4-5 


3 


5 


7 


10 


15 


0.122 


0.114 


0.093 


0.079 


0.066 


9 


12 


18 


25 


31 


30 


40 


60 


80 


100 


o.544 


0.053 


0.052 


0.051 


0.050 



FRICTION OF LUBRICATED SURFACES. 309 

At common, but somewhat slow, speeds he thus finds that 
the friction between pieces of pine-wood decreases rapidly 
as the speed increases. With the wrought-iron shaft of 1 inch 
(25 cm.) diameter, working in a cast-iron bearing, well oiled, 
an increase of velocity of rubbing from 6 to no feet (1.8 to 
33.5 metres) per minute caused the coefficient of friction to 
fall to 0.3 of its first value. The pressure in this case was 
about 67 lbs. per square inch (4.7 kgs. per sq. cm.). The other 
experiments on lubricated journals at smaller pressures gave 
the opposite result. 

Referring to the next table, p. 310, in which the effects of 
varying velocities, as well as of coincident variation of pres- 
sure and of temperature, are exhibited as given by experi- 
ments, it is readily seen that the change in value of the coeffi- 
cient of friction with change of velocity is not great for 
machinery in which that velocity remains within usual limits, 
and at the usual temperature of a cool and properly-working 
journal. The effect of change of velocity varies, as is here 
shown, with change of temperature and of pressure. 

Hirn's experiments indicate, as he has stated, that the fric- 
tion of lubricated surfaces is affected by velocity through 
variation of the quantity of oil drawn between them at vary- 
ing speeds. Even ak becomes thus a lubricant at very high 
speeds, producing exceedingly low values of the coefficient. 
The observations of Despretz lead to the same conclusions. 

For cool journals, in good condition, lubricated with good 
sperm-oil, and between the limits of 100 and 1200 feet (31 and 
370 m.) per minute, these values may be taken for ordinary 
lubrication, in estimating lost work and in designing, as vary- 
ing approximately as the fifth root of the velocity of rubbing, 
i.e.,/= a Wj in which a, at 200 lbs. per square inch (14 kgs. 
per sq. cm.), is about 0.0005 f° r ordinary lubrication, but may 
fall much lower with journals flooded by an oil-bath ; in the 
latter case, also, the coefficient increases very nearly as the 
square root of the speed. Both Professor Jenkin and the 
Author have deduced * from the fact that the coefficient of 

* Friction at High Velocities, Inst. Mechanical Engrs., 1879; Friction and 
Lubrication, 1879, p. 185. 



3io 



FRICTION AND LOST WORK. 



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FRICTION OF L UBRICA TED SURF A CES. 3 1 1 

friction of rest is always greater than that of motion, while the 
latter at low speeds steadily and constantly increases as the 
velocity of rubbing decreases, the conclusion that there is 
probably a continuous change resulting in the merging of the 
one in the other. Where the difference between the two coeffi- 
cients is small, that of motion is nearly constant at all interme- 
diate velocities. This conclusion is also reached by Mr. A. M. 
Wellington.* The Author has also found, by experiment, 
that the coefficient at high speeds steadily and continuously 
increases, and hence that there is a minimum value at some 
intermediate speed, the precise location of which minimum is 
determined by the pressure and the temperature. The ex- 
periments upon which the last table is based were made upon 
the same machine as those described previously, the journal 
of fine steel running in a good gun-bronze bearing, and in the 
manner described in the last chapter. 

The experiments of Poiree and Bochetf show, as already 
stated, that increase of speed .of rubbing decreases the friction- 
coefficient with unlubricated surfaces also ; this decrease be- 
tween the velocities of 900 and 3600 feet (270 and 1080 m.) 
being from 0.2 to 0.13, or about one third. The experiments 
of Galton and Westinghouse J confirm this conclusion. This 
method of variation has not been found to have a limit with 
dry surfaces ; but with lubrication, as above stated, the law 
changes at some point, and the minimum is found at a higher 
speed as the pressure on the rubbing surfaces increases. This 
latter conclusion is confirmed by later investigations. 

With heavy machinery, the pressure and speed varying 
simultaneously, we may take as an approximately correct ex- 
pression for flooded journals, 

w 

the value of a being usually between 0.015 and 0.02. 

* Trans. Am. Soc. C. E., 1884. 
fMem. de la Soc. des Ing. Civils, 1852. 
% Proc. Inst. Mechan. Engs., 1879. 



312 



FRICTION- AND LOST WORK, 



COEFFICIENTS OFTRICTION. 

120°& 180° 

.005./ ..010 .015 .020 .025 .030 .035 .040 .045 .050 .050 



1200 
SPEED IN FT? 

PER MIN. 

WOO 



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600 

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200 



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Fig. 48. — Velocity and 



Friction. 



FRICTION OF L UBRICA TED SURF A CES. 3 1 3 

With the more perfect lubrication attainable by the oil-bath 
the friction varies nearly as the square root of the speed, at 
velocities customarily met with in engineering. At very low 
speeds, as shown by the experiments already quoted, the coef- 
ficient decreases with increasing speed — presumably in conse- 
quence of the greater freedom of supply so secured. At speeds 
exceeding ioo to 150 feet (30 to 46 m.) per minute, the resist- 
ance increases slowly with ordinary lubrication, and more rap- 
idly with more perfect oil-supply. The experiments of the 
Institution of Mechanical Engineers give, for oil-bath lubrica- 
tion and flooded journals, approximately : 



Sperm-oil /oc . /_; 

w 



Lard-oil / oc 



P ' 



Olive-oil o a /oc —p-\ 

v~v~ 

Mineral-oil / oc ——. 

J pi 

The apparent law thus varies with the character of the 
lubricant, with variation of pressure, although usually giving 
values of friction varying as the square root of the velocity. 

The work of the Author, exhibited in Figs. 48, 49, illus- 
trates the peculiar variation of friction with velocity of rubbing, 
through a wide range of speeds, pressures, and temperatures. 
These curves, which were constructed for the Author by the 
late Mr. W. G. Cartwright, indicate the existence of a definite 
law of variation of the coefficient, for each definite set of con- 
ditions, taken as unvarying in other respects. At low speeds 
the coefficient decreases, in all cases, with great rapidity ; passes 
a minimum, usually at between 100 and 200 feet (30 and 61 m.) 
per minute, and then gradually increases again up to the high- 
est speeds attained. 

For sperm-oil, the increase at 100 lbs. per square inch (7 kgs. 
per cm.) is very uniform in these experiments, and is very 



314 



FRICTION AND IOST WORK. 



500 
SPEED IN FT. 

PER MIN, 

400 



COEFFICIENTS OFFRICTION 
.005 .010 .0T5 .050 .025 .030 .035 .040 .045 .050 




Fig. 49. — Velocity and Friction. 



FRICTION OF LUBRICATED SURFACES. 3 I 5 

nearly proportional to the increase of speed, but is most rapid 
at the lowest temperatures noted. The latter is the fact also 
at higher pressures ; but less difference is usually observed with 
change of temperature. 

Heavy petroleum, as shown in the last of these figures, ex. 
hibits the same general behavior at ioo and at 150 lbs. (7 and 
10 kgs. per sq. cm.) ; while at the lowest pressure, 50 lbs. per 
square inch (3.5 kgs. per sq. cm.), the action of varying temper- 
ature becomes exaggerated to such an extent as to become very 
plainly observable. It is seen that with such lubrication as was 
here obtained the best temperature for this pressure is the 
highest as usual, while at 90 the coefficients steadily increase 
from the lowest speeds. 

These curves are all established by too limited a set of ob- 
servations to permit definite formulation of results, and those 
presented must be received and used with caution until more 
work is done and these laws are more completely ascertained. 
As confirming the general deduction that the higher speeds 
met with in machinery give reduced coefficients, it may be stated 
that Mr. Pearce, of Cyfartha, reports less indicated power re- 
quired to drive an unloaded rolling-mill engine at high speeds 
than at low. 

140. Rest and Motion, not only as already stated, give 
coefficients of friction differing greatly in value ; but experiment 
indicates that they follow entirely different laws. The varia- 
tions of both coefficients will probably prove to be influenced 
by every change of condition of surface or of method of lubri- 
cation, or of operation. Figs. 50, 51, 52, exhibit graphically 
the results of experiments made on the testing-machine of the 
Author with a wide range of pressure, and the comparison of 
these coefficients when using sperm, lard, and mineral oils. 
The temperature was in each case 115 F. (46 C). 

Under the conditions of surfaces and of lubrication — by oil- 
cups — here adopted, the speed of rubbing being 150 feet (46 
m.) per minute, the sperm-oil (Fig. 50) exhibits a minimum co- 
efficient at 400 to 500 lbs. per square inch (28 to 35 kgs. per sq. 
cm.), while the coefficient for rest rises very rapidly as pressures 
increase toward 100 lbs. (7 kgs.), less rapidly to 500 lbs. (35 kgs.), 



316 



FRICTION AND LOST WORK. 



PRESSURE IN LBS. PER SQ. INCH 



100 200 300 400 500 600 700 800 900 1000 


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COEFFICIENTS 












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Fig. 50. — Friction of Rest and Motion. 



FRICTION OF LUBRICATED SURFACES. 



317 



100 



PRESSURES IN LBS. PER S9.J.NCH 
200 300 400 500 600 700 800 900 1000 



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COEFFICIENTS 
OF FRICTION 

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Fig. 51. — Rest and Motion. 



318 



FRICTION AND LOST WORK. 



PRESSURE IN LBS. PER Sj?, 04C.H 
100 200 300 400 500 600 700 800 900 1000 


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Fig. 52.— Rest and Motion, 



FRICTION OF LUBRICATED SURFACES. 319 

more rapidly again to 750 lbs. (52.5 kgs.) ; while the last obser- 
vation at 1000 lbs. per square inch (703 kgs. per sq. cm.) gave a 
lower figure, which however may have been an accidental and 
exceptional departure from the general law. 

Lard-oil (Fig. 51) exhibited the same behavior when in mo- 
tion, passing the minimum at the same pressure, and having then 
3. little higher value. The coefficient for rest also varies at the 
start in exactly the same manner, rapidly increasing with rise 
of pressure up to 100 lbs. per square inch (7 kgs. per sq. cm.) as 
before ; but it then decreases with rising pressures, passing the 
maximum at about 150 lbs. (10 kgs.), and a minimum at 500 
lbs. (35 kgs.), and rising to a second maximum at highest pres- 
sures. 

The general character of the curve is the same as that for 
sperm-oil, but with the terminal portion depressed. 

Heavy lubricating petroleum behaved (Fig. 52) very much 
like sperm-oil passing the minimum on the moving journal ; at 
a somewhat higher figure (750 lbs. ; 53 kgs.) it gives exactly the 
same form of curve of coefficients for rest that was obtained 
with sperm ; and the lines for the two oils are almost identical 
in location. It is thus evident that these peculiar curves are 
not obtained by a merely accidental set of conditions for either 
oil. 

In these experiments the minimum coefficients for motion 
were for sperm 0.004, f° r lard-oil 0.005, an d for mineral oil the 
same as lard. At the same pressures the coefficients for quies- 
cence were 0.15, 0.10, 0.15 for the three oils. Lard-oil permits 
starting most easily, but it loses its superiority as soon as 
motion begins. 

These relations of value probably differ, however, with every 
change of speed and temperature as well as of pressure. 

141. Temperature modifies Friction to a very important 
degree, as is seen by examining the tables already given, and 
especially by studying the following values, which were ob- 
tained by heating the bearing by its own friction to a maxi- 
mum 170 Fahr. {yj C), well within that liable to produce al- 
terations of the oil, and then noting the friction at successive 
decreasing temperatures while cooling. It should be remem- 



2,20 FRICTION AND LOST WORK, 

bered that no temperature-readings can be taken as more than 
approximate. 

Friction and Temperature. 



Steel Journals. 


Lubricant, 


Sperm Oil. Velocity, 30 feet per minute. 


Pressure, lbs. per 
square inch. 


Temperature, Fahr. Coefficient of Friction: /i 


200 




150 0.0500 


200 




140 0.0250 


200 




130 0.0160 


200 




120 O.OIIO 


200 




no 0.0100 


200 




100 0.0075 


20O 




95 . 0060 


200 




90 0.0506 


I50 




no 0.0035 


IOO 




no 0.0025 


50 




no 0.0035 


4 




no 0.0500 


200 




90 . 0040 


I50 




90 0.0025 


IOO 




90 0.0025 


50 




90 0.0035 


4 




90 0.0400 



The figures just given would indicate that the sperm-oil 
used in this instance, and under these conditions, including 
that of exceptionally low speed, works best at lowest tempera- 
tures, and that a heating journal gives rapidly increasing fric- 
tion and rapidly increasing danger. At usual temperatures — 
90 to 1 io° F. (32 to 43 C.) — the best pressure seems to have 
been from 100 to 150 lbs. on the square inch. The study 
of the last table is exceedingly interesting and instructive. 
There are there given coefficients of friction for temperatures 
from 90 to 150 F., for pressures up to 200 lbs. per square 
inch, and for velocities of rubbing up to 1200 feet per minute. 

It has been seen that at the low speed of 30 feet (9 m.) per 
minute, the coefficient increases rapidly with increase of tem- 
perature, and that at 200 lbs. pressure (14 kgs.), an increase of 
50 F. (io° C.) may increase its value to nearly ten times the 
minimum, the rate of increase rapidly rising as pressures are 
greater. 



FRIC TION OF L UBRICA TED S URFA CES. 3 2 1 

It is now found, at speeds of 100 feet (31 m.) per minute, 
that the friction does not vary between 90 and 150 F. (32 
and 66° C), at pressures below 50 lbs. per square inch (3.5 kgs. 
per sq. cm.) ; but that it rises nearly 300 per cent, at a pres- 
sure of 200 lbs. (14 kgs.), over 100 per cent, at 150 lbs. (11 kgs.), 
and 33 per cent, at 100 (7 kgs. per sq. cm.). 

At speeds exceeding 100 feet (31 m.) per minute, heating 
the journal within this range of temperature decreases the re- 
sistance due to friction, rapidly at first ; then, slowly and 
gradually, a temperature is approached at which increase takes 
place and progresses at a rapidly accelerating rate. It is seen 
that this change of law takes place at a temperature of 120 
F. (49 ° C), and upward ; at all higher speeds the decrease con- 
tinues until temperatures are attained exceeding those usually 
permitted in machinery and very commonly not far from 150 
F. (66° C), and sometimes up to 180 F. (82 C), or probably 
even higher. The Author has found the decrease at 1200 feet 
(37 m.) per minute to continue up to 175 F. (79 C), at which 
the value, at 200 lbs. (14 kgs.) pressure, was, in the cases deter- 
mined, 0.0050. The limit of decrease is reached under 100 
lbs. (7 kgs.) pressure, at 150 F. (66° C), when running at this 
high speed. 

At 200 lbs. (14 kgs. per sq. cm.) pressure, the temperature 
of minimum friction for conditions here illustrated seems to be, 
in Fahrenheit degrees, about 

t=\^s/T. 

On either side this point on the thermometric scale it may 
be assumed, for a narrow range, to vary, as the temperature de- 
parts from that point, directly or inversely, as the case may 
be, as the temperature. The coefficient of minimum friction 
is found usually nearly constant over quite a wide range of 
temperature. 

Again, studying in this most instructive of these tables the 
method of variation with pressure at higher temperatures, we 
find the effect of change of pressure to be much more marked 
at the higher temperatures at low speeds ; and we note, as 
when studying the effect of variations of friction with change 



322 FRICTION AND LOST WORK. 

of temperature at a standard pressure as affected by variation 
of speed, that we here find a change of law for the higher 
speeds. 

At a velocity of 1200 feet (37 m.) per minute, the coefficient 
remains practically uniform with varying pressure at 150 F. 
(66° C), while below that temperature the friction coefficient 
diminishes with increasing pressure. At velocities of rubbing 
of 250 to 500 feet (75 to 150 m.) per minute the temperature 
of the constant coefficient is about ioo° F. (38 C.) ; at 100 feet 
(31 m.) this peculiar condition is seen at about 1 20° F. (49 C), 
when extreme pressures (4 to 200 lbs., 0.28 to 14 kgs.) are 
compared, but the value is seen to be a little over one half as 
much at 50 and 150 lbs. (3.5 and 1 1 kgs.), and to become a mini- 
mum — 0.0019 — at 100 lbs. (7 kgs.) pressure; a similar behavior 
is noted at the lowest speed observed — 30 feet (9 m.) — at about 
125 F. (52 C), and the same fall to a minimum occurs at the 
intermediate pressure. It would seem that at all times there 
is a tendency to an acceleration of outflow from the journal, 
with increase of fluidity due to increasing temperature, 
which tends to cause an increase of friction, while the effort 
of capillarity to resist this outflow seems effectively aided by 
increasing the velocity of rubbing. A balance between these 
opposite influences is seen to take place at the slowest speed 
when the pressure is somewhere below 4 lbs. per square inch 
(0.28 kgs. per sq. cm.) ; this occurs at a speed of 100 feet (36 m.) 
per minute at a pressure of 50 lbs. (3.5 kgs.), at 250 feet (yy m.) 
when the pressure becomes about 150 lbs. (11 kgs.) probably ; 
it happens at a speed of 500 feet (155 m.) at somewhere about 
the same point ; and at 1200 feet (37 m.) per minute the bene- 
fit of increased speed is sufficient to produce this balance when 
the pressure exceeds 200 lbs. per square inch (14 kgs. per 
sq. cm.). 

142. The Law of Variation of Friction with Tempera- 
ture is evidently not a simple and definite one. 

Studying all the results obtained, as above, it becomes evi- 
dent that every pressure demands a certain degree of viscosity 
and capillarity in the lubricant to secure at the same time 
thorough lubrication and minimum friction. The effect of 



FRICTION OF LUBRICATED SURFACES. 



323 



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Fig. 53. — Friction and Temperature. 



EKD OF VOL. I. 



3 2 4 



FRICTION AND LOST WORK 



variation of temperature is to produce alteration of viscosity, 
and with low pressures decreased resistance and lessened fric- 
tion ; while with high pressures the effect of increased tempera- 
ture is to carry the unguent beyond the point at which it can 
be retained between the surfaces. Thus, at 5 lbs. per square 
inch (0.35 kgs. per sq. cm.) castor-oil is a very inefficient lubri- 
cant at ordinary temperatures ; but it becomes equal to the 
best mineral oils at 200° F. (93 C). Every oil thus has a 
maximum value, for each pressure, at a certain definite tempera- 
ture, and at certain temperatures, 
different for each, all common 
oils have the same coefficient. 
Tims, sperm at about ioo° F. 
(38 C), a light mineral oil at 
the same temperature, a heavy 
mineral oil at 125 F. (52 C), 
neat's-foot at 170 F. (yy° C), and 
lard-oil at 180 F. (82 C), all 
have the same coefficient, accord- 
ing to Woodbury, at spindle- 
pressures. At this light pres- 
sure, lard-oil at 130 F. (54 C.) 
^ lubricates as well as sperm at 
Friction and Tempera- 70 F. (21 C), or the best refined 
TURE - petroleums at 50 F. (io° C). 

Fig. 53 exhibits the behavior of mineral, sperm, lard, and 
neat's-foot oils with varying temperature, as given by Mr. 
Waite. These curves are very similar to those exhibiting the 
relation of viscosity and temperature ; but, like the others just 
given, only relate to very low pressures. Under such light 
loads as are usual in spinning-frames, the resistance decreases 
very nearly as the temperature rises, within the limits here ex- 
hibited. The same facts are exhibited also in Fig. 52, in which 
the variation of the coefficient, as observed by Woodbury, is 
shown for several pressures between 1 and 40 lbs. per square 
inch (0.07 to 3.5 kgs. per sq. cm.). 

The method of variation of the friction with temperature 
is shown in Fig. 54 also. 



130 




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326 



FRICTION AND LOST WORK. 



In Fig. 55, this variation of friction with temperature is 
traced still further, and the general character of the law in- 
volved is still better seen than before. 



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PRESSURE 33 LBS. PER SQ. INCH. > 


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COEFFICIENT OF FRICTION 



Fig. 56. — Friction and Temperature. 



At low temperatures, the figure shows the large coefficient 
of friction due to viscosity of the oil, while the rise in friction 
at higher temperatures indicates a resistance produced by the 
collision of portions of the disks, and the diagram, Fig. 56, is a 
graphical representation of the production of a hot bearing. 



FRICTION OF LUBRICATED SURFACES. Z 2 7 

It is evident that the best lubricant for a bearing in good 
order is not necessarily the best for a hot journal. The viscous 
oils and greases, which are comparatively wasteful of power 
under ordinary conditions, are good unguents for a heating or 
a chronically hot journal. Castor-oil may be excellent for a 
hot journal, while kerosene of the lightest grade is best for the 
chilled surfaces of the cylinder of the compressed-air engine, or 
the rock-drill. A difference of 50 per cent, may be observed 
in driving light machinery at temperatures of 50 F. and 75 
F. (io° and 24 C), and the cost in winter of keeping a mill 
well warmed may be paid for by the reduction in waste of 
power so produced. The effect of varying temperature is seen 
equally well in the curves of Fig. 57, which represent the 
experiments of Hirn, made at low pressures (1.4 lbs. per sq. 
in. ; 0.1 kg. per sq. cm.). The coefficient rapidly falls, as tem- 
perature rises from a very low temperature up to the boiling- 
point of water, and by a peculiar law of variation ; from that 
point it decreases less rapidly, finally varying inversely as the 
temperature. The record of tests of " cylinder oils" given in 
article 136 illustrates this phenomenon most strikingly. 

The experiments of the Author are shown in Figs. 58 and 
59, and present to the eye the method of variation of friction 
with temperature at more usual pressures, and at various speeds 
ranging from 30 to 1200 feet per minute (9.1 to 366 metres). 
At the lowest speeds, the friction rapidly increases with 
increase of temperature, at all pressures from 50 to 200 lbs. 
per square inch (3.5 to 14 kgs. per sq. cm.), varying very 
nearly as the temperature up to 120 or 130 F. (49 to 
54° C.) ; it then increases more nearly as the square of the 
temperatures. As the pressures and speeds increase, the 
curves and the law of variation change, until, at 1200 feet per 
minute (366 m.), sperm-oil exhibits much less friction at high 
temperatures, and very nearly the same behavior at all pres- 
sures. At speeds ranging from 100 to 500 feet per minute (30 
to 152 m.), alteration of temperature has little effect, where 
the oil is fed, as here, by the usual system. With the oil-bath 
and a flooded journal, as seen later, the effect of temperature 
is very different, and a very great reduction of friction follows 



328 



FRICTION AND LOST WORK. 






moderate increase above common temperatures. On the 
whole, it is evident that, at the speeds and pressures usual in 
machinery, the resistance decreases as the journals and bear- 
ings warm up; and this decrease continues beyond the limit 
which the engineer considers it best to set to such heating. 



COEFFICIENTS OF FRICTION 
0.05 0.J0 011.5 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 


600 ' " l | 










1 1 I ( II II II II II 


Ri X 










MINIMI 




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± t 




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200 ' \ _ \. . 




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Fig. 57. — Temperature and Friction. 

Fig. 59 shows the same effects when the lubricant is a 
heavy mineral oil. The same general behavior observed al- 
ready is here seen. The oil, at the low speeds experimented 
with, exhibits rapidly increasing friction, with increase of tem- 
perature, while at the higher speeds the coefficient rapidly 
decreases. With this oil the coefficient is constant at some 
speed lying between 50 and 100 feet (15 and 30 m.) per min- 






FRICTION OF LUBRICATED SURFACES. 



329 



COEFFICIENTS OF FRICTION 
.005 .010 .015 .020 .025 .030 .035' .040 .045 .050 .055 


TEMP. " " -)&& jbr 5 ^'' "jZ '" -''"* 






10U ' 7'S* 4S2* J U- -" 


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Fig. 58. — Temperature and Friction. 



33Q 



FRICTION AND LOST WORK. 



ute. At 250 feet per minute, change of pressure seems in 
these experiments to have little effect upon the behavior of 
the oil in this respect. 

As the efficiency of the lubrication improves, as is evident 
from experiments made with the oil-bath, the coefficient of 
friction decreases at ordinary temperatures ; while the sensi- 
tiveness to variation of temperature rapidly increases, the 

COEFFICIENTS OF FRICTION 

,0 005 .01 015 .Q20'-025 .030 .035 .040 .045 .050 .055 .060 .065 .070 .075 .080 .085 .090 




Fig. 59. — Temperature and Friction. 

reverse being noted as effectiveness of lubrication diminishes. 
But the speed of the journal is an important element, and the 
higher the velocity, the oil being freely supplied, the more 
perfect the separation of the metal surfaces by the intervening 
cushion or layer of oil. Thus it happens that at low speeds, 
as 30 to 50 feet (9 to 15 m.) per minute, the lubrication is not 
only inefficient at moderate pressures, but becomes rapidly 



FRICTION OF LUBRICATED SURFACES 



331 



more so under higher pressures, and the coefficient increases 
with rise of temperature toward a limit at which abrasion 
probably takes place. On the other hand, with oil-bath lubri- 
cation, the friction varies very exactly as the square root of 
the speed. 

The work of the Institution of Mechanical Engineers has 
been reduced and illustrated graphically, as below (Fig. 60), 































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VELOCITY— MILES PER HOUR. 

Fig. 60. — Train Resistance. 



by Mr. A. M. Wellington, assuming oil-bath lubrication possi- 
ble in railway service. 

The resistance is reduced to pounds per ton, the usual 
method of statement in railroad work. It is here very well 
shown that at all usual speeds, with such exceptional lubrica- 
tion, the resistance increases with speed, rising from 1 lb. per 
ton at 20, to if at 50 miles per hour, when the load is 100 
lbs. per square inch. At double this pressure and upward, the 
same law holds, the resistance falling, however, as the inten- 
sity of pressure increases. 

The effect of variation of speed in ordinary railway practice 



332 



FRICTION AND LOST WORK. 



is well shown in the diagram given below (Fig. 61), of results 
obtained by Mr. Wellington.* The intensity of the pressure 
per square inch of journal (longitudinal section) is indicated 
graphically thus : 



23(jj-- ■ | 




or 


1EAVIEST LOAD, 279 LBS. PER SQ.IN. 




-lo 




~T7S_ 






MEDIUM » 154 '• " 






UJl 






-IGHT » 29 " " 


M-UlV 




1 Yl"l\ 




Vmyi HIQHES" 


" LINE OF EACH. JOURNAL H0T,120° TO 150° F. 


^CtfsX^ 




■11 VI A\ 




'.)i V »> \ i nwEST 


" " » C00L.UNDER 100 F. 






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■ \a \v\ ^ 




! v^ - vs. ^ 




1 o " V ^ \ 




^%X-\ ^^ ^ 




J_J \ \ V 




1 V \ ^ 








■ I v \ \ "^ 




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■% A^ % ^v 








^ V ^ "i 




V K V. 




\ \ V c -- — , 


r— _ 


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V ^* 


"t^f^e: _c=p±=L^= e _ r jm===L s2 _ 




~~ ■ — i <-) 






T°~ 
































12 3 4 


6 7 8 9 10 31 - 12 



Fig. 6i. 



velocity — miles per hour 
Results of Wellington's Tests. 



The friction falls with decreasing speed, rapidly at first, 
then more slowly as the train gradually comes to rest from the 
speed commonly adopted in freight traffic. 

143. Later Researches, corroboratory of the statements 
of fact and of the deductions presented in the preceding 
pages, have been made by many investigators. Mr. Beau- 
champ Tower, some of whose work has been given, conduct- 
ing experiments, in 1883, for a committee of the British 
Institution of Mechanical Engineers, f obtained the same 
general results as had the Author, using a machine of very dif- 
ferent construction, with which the pressure was produced by 



.* Trans. Am. Soc. C. E., 1884. 
I Reports of Committee on Friction, 1884. 



FRICTION OF LUBRICATED SURFACES. 333 

weighting the journal and the friction determined by the use 
o£ a brake somewhat resembling that of Prony, the indications 
of which were recorded automatically, as had been done by 
Lux. 

In most cases the lubricant was fed to the journal, which 
was of car-axle size, by the use of a " bath," by means of 
which the journal could be kept flooded constantly, the friction 
being thus reduced, as has been elsewhere stated (§ 133), to a 
small fraction of that met with under more common arrange- 
ments. With the more usual system of lubrication, as re- 
ported, the results, generally speaking, were uncertain and 
irregular. The friction depends, in such cases, on the quantity 
and uniformity of distribution of the oil, and " may be any- 
thing between the oil-bath results, and seizing, according to 
the perfection or imperfection of the lubrication." The oil-bath 
probably represents the most perfect lubrication possible, and 
the limit beyond which friction cannot be reduced by lubrica- 
tion ; and the experiments show that with speeds of from 100 
to 200 feet per minute, by properly proportioning the bearing 
surface to the load, it is possible to reduce the coefficient of 
friction as low as 1 ^ . A coefficient of -5-^ is easily attain- 
able, and probably is frequently attained, in ordinary engine- 
bearings in which the direction of the force is rapidly alternat- 
ing." 

With this system the speed of minimum friction was ap- 
parently between 100 and 150 feet (30 and 46 m.) per minute. 

When using a pad to apply and distribute the oil, the 
friction showed some approach to variation according to the 
laws of solid friction. Using the siphon, or ordinary feed-cup, 
the variation followed very nearly the same law as with the 
bath, as is also seen by a comparison with the results recorded 
by the Author. The succeeding tables, given in the report of 
the committee, represent the more important results. The 
journal was kept at a temperature of 90 F. (32 C). 



334 



FRICTION AND LOST WORK. 



FRICTION OF LUBRICANTS. 
Bath of Sperm Oil. 



Nominal Load. 




Coefficients of Friction, for Speeds as below. 




Kgs. per 
sq. cm. 


Lbs. per 

sq. in. 


100 rev. 

105 ft. 
per min. 
(32 m.) 


150 rev. 
i57 ft-, 
per mm. 
(48 m.) 


200 rev. 
209 ft. 
per min. 
(64 m.) 


250 rev. 
262 ft. 
per min. 
(79 m.) 


300 rev. 
314 ft. 
per min. 
(95 m.) 


350 rev. 
366 ft. 
per min 
(112 m.) 


400 rev. 
419 ft. 
per min 
(128 m.) 


450 rev. 
471 ft. 
per min. 
(143 m.) 


36 
29 


520 
415 
310 

205 

i53 

100 


Seized 
















0.0015 

O.OOII 

0.0016 
0.0019 
0.003 


0.0017 
0.0012 
0018 
0.0023 
0.0038 


0.0018 
0.0014 
0.0021 
0.0028 
0.0044 


0.0019 
0.0016 
0.0023 
. 0030 
0.0051 


0.002 
0.0017 
. 0024 
0.0033 
0.0057 


0.0021 
0.0018 
0.0025 
0.0035 
0.0061 


0021 




0.0019 
. 0027 
0.0037 
. 0064 


14 
10 
7 


0.0013 
0.0016 
0.0025 



Bath of Lard Oil. 



Nominal Load. 



Coefficients of Friction, for Speeds as below. 



Kgs. per 
sq. cm. 



Lbs. per 
sq. in 



100 rev. 
105 ft. 
per min. 
(32 m.) 



150 rev. 
157 ft. 
per min 
(48 m.) 



200 rev. 
209 ft. 
per min. 
(64 m.) 



250 rev. 
262 ft. 
per min. 
(79 m -) 


300 rev. 
314 ft. 
per min. 
(95 m.) 


350 rev. 
366 ft. 
per min. 
(112 m.) 


400 rev. 
419 ft. 
per min. 
(128 m.) 


O.OOII 

0.0015 
0.002 
. 0028 
. 0037 
0.006 


0.0013 
0.0016 
0.0022 
0.0031 
0.0041 
0.0067 


0.0015 
0.0018 
0.0025 
. 0034 
0.005 
0076 


0.0015 
0.0019 
0.0026 
0.0039 
0.0051 
0.0081 



450 rev. 
471 ft. 
per min. 
(143 m.) 



520 

4 X 5 
310 
205 

153 
100 



0.0017 
0.0022 
0.0035 



0.0009 
0.0012 
0.0014 
0.0020 
0.0027 
0.0042 



O.OOI 

0.0014 
0.0017 
0.0023 
0.0032 
0.005 



0.0017 
0.0021 
0.0029 
o . 0042 
0.0052 
0.009 



Bath of Rape Oil. 



Nominal Load. 


Coefficients of Friction, for Speeds as below. 


Kgs. per 
sq. cm. 


Lbs. per 
sq. in. 


100 rev. 
105 ft. 
per min. 
(32 m.) 


150 rev. 
157 ft. 
per min. 
(48 m.) 


200 rev. 
209 ft. 
per min. 
(64 m.) 


250 rev. 
262 ft. 
per min. 
(79 m.) 


300 rev. 
314 ft. 
per min. 
(95 m.) 


350 rev. 
366 ft. 
per min. 
(112 m.) 


400 rev. 
419 ft. 
per min. 
(128 m.) 


450 rev. 
471 ft. 
per mm. 
(143 m.) 


4 « 
36 

32 

25 

18 

10 

7 


573 
520 
4i5 
363 
258 

iS3 
100 




0.00102 

0.000955 

0.00093 

0.00084 

0.00139 

0.0020 

0.00357 


0.00108 

0.00105 

0.00107 

. 0096 

0.00162 

0.00239 

0.00423 


00 U") On 00 t>. ro 
H H M H C^NO 
M H M H H CN1 IO 

O08080O 

6 6 6 6 6 6 6 


0.00126 

0.00125 

0.0013 

0.00122 

0.00195 

0.003 

0.00576 


0.00132 
0.00133 
0.00140 
0.00134 
0.00213 
0.00334 
0.00619 


00139 
0.00142 
0.00149 
0.00147 
0.00227 
0.00367 
0.00663 






0.00148 
0.00158 
0.00155 
0.00243 
0.00396 
0.00714 






0.00107 
0.00162 
0.00277 



FRICTION OF LUBRICATED SURFACES. 



335 



Bath of Olive Oil. 



Nominal Load. 


Coefficients of Friction, for Speeds as below. 


Kgs. per 
sq. cm. 


Lbs. per 
sq. in. 


100 rev. 
105 ft. 
per min. 
(32 m.) 


150 rev. 200 rev. 

157 ft. 1 209 ft. 
per min. per min. 
(48 m.) | (64 m.j 


250 rev. 
262 ft. 

per min. 
(79 m.) 


300 rev. 
314 ft. 
per min. 
(95 m.) 


350 rev. 
366 ft. 
per min. 
(112 m ) 


1 
400 rev. 450 rev. 
419 ft. i 471 ft. 
per min. per min. 
(.128 m.) , (143 m.) 


36 
32 
29 
25 


520 
468 
415 
363 
310 
258 
205 

i53 
100 




0.0008 

O.OOII 

0.0012 

0.0013 

0.0015 

0017 

0.0021 

0.003 

0.0045 


OOI 

0.0013 

0.0014 

0.0016 

0.0017 

0.002 

0.0025 

0.0035 

0.0055 


0.0012 

0.0014 

0015 

0.0017 

0.0019 

0.0023 

0.0028 

0.004 

0.0063 


0.0013 
0015 
0.0017 
0.0019 
0021 
0025 
0.003 
0.0044 
0.0069 


0.0014 

0.0017 

0.0019 

0.002 

0.0022 

0.0026 

0.0033 

0.0047 

0.0077 


0.0015 0.0017 
0.0018 , 0.002 




0.0022 

0.0024 

0029 

0.0036 

0.005 

0.0082 


0.0025 

0.0027 

0.0031 

0.004 

00057 

0.0089 


18 
14 
10 
7 


0.0014 
0.0018 
0.0023 
0.0036 



Bath of Mineral Oil. 



Nominal Load. 




Coefficients of Friction, for Speeds 


AS BELOW. 




Kgs. per 
sq. cm. 


Lbs. per 

sq. in. 


100 rev. 
105 ft. 
per min. 
(32 m.) 


150 rev. 

i57 ^. 
per min. 
(48 m.) 


200 rev. 
209 ft. 
per min. 
(64 m.) 


250 rev. 
262 ft. 
per min. 
(79 m.) 


300 rev. 
314 ft. 
per min. 
(95 m.) 


35° rev. 
366 ft. 
per min. 
(112 m.) 


400 rev. 
419 ft. 
per min. 
(128 m.) 


44 
36 
29 


625 
520 
415 
310 
205 
100 




0.0013 

0.00123 

0.00123 

0.00x42 

0.00205 

0.00415 


0.00139 

0.00139 

0.00143 

0.0016 

0.00235 

0.00494 


0.00147 

0.0015 

0.0016 

0.00184 

0.00269 

0.00557 


0.00157 
0.00161 
0.00176 
0.00207 
0.00298 
0.0062 


0.00165 

0.0017 

0.0019 

0.00225 

0.00328 

0.00676 






0.00178 






0.00241 

0.0035 

0.0073 


14 
7 


0.00178 
0.00334 



Bath of Mineral Grease. 



Nominal Load. 



Kgs. per 
sq. cm. 



Coefficients of Friction, for Speeds as below. 



100 rev. 
Lbs. per 105 ft. 
sq. in. per min. 

(32 m.) 



625 
520 
415 
310 
205 
z 53 
100 



0.002 
0.0026 
0.0028 
0.0054 



150 rev. 
157 ft. 

per min 
(48 m.) 



O.OOI 

0.0014 
0.0016 
0.0022 
o 0034 
0.0038 
0.0076 



200 rev. 


250 rev. 


300 rev. 


209 ft. 


262 ft. 


314 ft. 


per min. 


per mm. 


per min. 


(64 m.) 


(79 m.) 


(95 m.) 


0.0012 


0.0014 


0.0014 


0.0016 


0.0018 


0.0019 


0.0019 


0.0021 


0.0023 


0.0026 


0.0029 


0.0032 


0.0040 


0.0047 


0.0053 


0.0048 


0.0057 


0.0065 


0.0094 


0.0109 


0.0123 



350 rev. 
366 ft. 
per min. 
(112 m.) 



0.0016 

0.002 

0.0025 

0.0035 

0.0058 

0.0071 

0.0133 



400 rev. I 450 rev. 

410 ft. 471 ft. 
per min. per min. 
(128 m.) (143 m.) 



o.ooi8 
0.0021 
0.0026 
0.0038 
0.0062 
0.0077 
0.0142 



0.002 

0.0022 

0.0027 

o 004 

0.0066 

0.0083 

0.0151 



The effect of change in the method of oiling is seen in the 
next two tables, taken in comparison with that above, giving 
the friction of the same lubricant when applied by the bath : 



33^ FRICTION AND LOST WORK. 

FRICTION WITH DIFFERENT SYSTEMS OF OILING. 
Rape Oil, Fed by Siphon Lubricator. 



Nominal Load. 


Actual Load. 


Coefficients of Friction, for Speeds as below. 


Kgs. 

per 

sq. cm. 


Lbs. 
per 

sq. in. 


Kgs. 
per 

sq. cm. 


Lbs. 

per 

sq. in. 


100 rev. 
105 ft. 
per min. 

(32 m.) 


> .So 

2d a a 


200 rev. 
209 ft. 
per min. 
(64 m.) 


> .So 

2d a a 

O N I- On 
"->VO V *"* 


> .So 

2d a a 

tJ-Vh in 

H <U On 
ro ro Q. w 


> .a 2 

Ovo h 2 

ro^aw 


2d B a 
8 S-fe H 


18 
i4 
7 


258 
205 
100 


22 
18 
8 


317 
252 
123 


0.0132 
0.0144 


0.0056 
. 0098 
0.0125 


0.0057 

0.007 

0.0146 


. 0063 
0.0077 
0.0152 


0.0068 
0.0082 
0.0163 


O.O087 
O.OI71 




O.OI78 



Rape Oil, Pad under Journal. 



Nominal 
Load, 


Actual 
Load. 


Tempera- 
ture. 


Coefficients of Friction, for Speeds as below. 


U 

. 

w . 
biocr 1 


Is 
3 M 


u 

&a 

. u 

to . 

oxer 


o-.S 


> ..So 

2s a a 

O m v- n 

O O <U ro 

h m a— - 


> .So 

Sid a a 

O t^Vn 00 

iflmu * 

H M Q^ 


> ..So 
2£8 8 

O OM- ■* 

«>o 


> ..So 
2^8 8 

O N U ON 
lOVO V tv 


> .So 

2d a a 

O •<*■ u m 

H D ON 

roroa^ 


^ c'o 

2d a a 

VO U „ 
IOVO 1) H 

ro ro qi,w 


> ..£7 

2d a a 

8 ?fe s 


24 


328 
310 
293 
275 
258 
205 

153 
100 


40 
38 
36 
35 
32 
25 
19 
12 


582 
551 
520 

498 
458 

364 

272 

178 


C. F. 

32° 90° 
28° 82° 
24° 76° 

25° 77° 
26° 78° 
28° 82° 
23° 74° 
24° 75° 






O.OIO7 
O . OO99 
O.OI05 
O.OOgi 
O.OO95 
O.O087 
O.OO96 
O.OIO9 


0.0102 
0.0092 
0.0097 
0.0095 

0.0088 

0.0085 
0.0102 
O.OI22 


O . O098 
O . 0099 
O.OO97 
O.OIO3 
O 0084 
O 0078 
0.0105 
O.OI33 




O.OI02 
0.0105 


O . OO99 

O.OIO5 

O.OO9I 

O.OII2 

O.OIO5 

O.OO9 

O . OO99 












19 
18 
14 

10 

7 






0.0082 
O . 0085 
0.0119 
O.0144 


0.0083 

O.OI 

0.0125 
0.0154 



The following table illustrates the variation of friction with 
alteration of temperature through a limited range. The re- 
sistance decreases enormously, in this case, with a moderate 
rise in temperature, becoming but one third the maximum. 



FRICTION AND TEMPERATURE. 

Bath of Lard Oil. Load, 100 lbs. per sq. in. (7 kgs. ptr sq. cm.) 







Coefficients 


3F Friction, for Speeds as below. 






100 rev. 


150 rev. 


200 rev. 


250 rev. 


300 rev. 


350 rev. 


400 rev. 


450 rev. 


Tempera- 


105 ft. 


i57 ft. 


209 ft. 


262 ft. 


314 ft. 


366 ft. 


419 ft. 


47i ft. 


ture. 


per min. 


per min. 


per min. 


per min. 


per min. 


per min. 


per min. 


per min. 




(30 m.) 


(18 m.) 


(61 m.) 


(79 m.) 


(95 m.) 


(113 m.) 


(128 m.) 


(143 m.) 


C F. 


















49° 120° 


0.0024 


0.0029 


0.0035 


0.004 


. 0044 


. 0047 


0.0051 


0.0054 


43 ° 110° 


0.0026 


0.0032 


0.0039 


0.0044 


0.005 


0.0055 


0.0059 


0.0064 


38° 100° 


0.0029 


0.0037 


0.0045 


0.0051 


0.0058 


0.0065 


0071 


0.0077 


32° 90° 


0.0034 


. 0043 


0.0052 


0.006 


. 0069 


0.0077 


0.0085 


. 0093 


27° 8o° 


0.004 


0.0052 


0.0063 


0.0073 


0.0083 


0,0093 


0.0102 


0.0112 


21° 70° 


0.0048 


0.0065 


0.008 


. 0092 


0.0103 


0.0115 


0.0124 


0.0133 


16° 6o° 


0.0059 


0.0084 


0.0103 


0.0119 


0.013 


0.014 


0.0148 


0.0156 



FRICTION OF LUBRICATED SURFACES. S37 

The oil-bath used in these experiments by Mr. Tower is 
not in common use, and cannot always be adopted when de- 
sired. The conditions are not, therefore, those of usual prac- 
tice ; but they may be taken as representative of conditions 
toward which practice should be made to approximate as 
closely as possible. It is seen that the mixed friction, here 
met with, approaches more nearly fluid friction than is 
usual. 

Other experiments, reported later by Mr. Tower, exhibited 
fluid pressures between journal and bearing rising to 625 
lbs. per square inch (43 kgs. per sq. cm.), and varying in 
very nearly the same ratio from the centre-line of the crown 
" brass," either way to the edge. The journal was found to 
be thus completely " oil-borne" at speeds as low as 20 revolu- 
tions per minute. The coefficient of friction at the latter 
speed was found to vary nearly inversely as the pressure, ex- 
hibiting a minimum at maximum nominal pressure, 443 lbs. per 
square inch (31 kgs. per sq. cm.), as follows: 



COEFFICIENTS OF FRICTION. 

Journal 4 inches diameter, 6 inches long. Revolutions per minute, 20; 21 feet 
per minute (61 m.) speed of rubbing j 90 F. (32 C), Mineral Oil. 

Nominal Load. 

Lbs. per sq. in. Kgs. per sq. cm. / 

443 31 O.OOI32 

333 23 0.00168 

211 15 0.00247 

89 6 o . 00440 



The experiments just summarized were all made at the 
high pressures usual in heavy machinery. The accompanying 
table of coefficients obtained by Woodbury at light pressures, 
and of which the graphical representation has already been 
given (§142), are very complete, and are valuable as comple- 
mentary of the work of other engineers on heavy work. The 
same general laws are here exhibited, and these values, with 
those already given, furnish a valuable set of data. 



338 



FRICTION AND LOST WORK. 



FRICTION OF PARAFFINE OIL. 

Velocity of rubbing, 300 feet per minute. 

Flash '. 342 Fahrenheit. 

Fire 4 IO ° " 

Evaporation by exposure to 140 Fahr. for twelve hours 0.02 

Specific gravity . 0.888 



« . 2 


Temperatures. 






Pres 

IN ] 

PER s< 


40° 


'45° 


5o° 


55° 


6o° 


65° 


7o° 


75° 


8o° 


85° 


90° 


95° 


IOO° 




Coefficient of Friction. 


I 


0.5380 


0.4760 


0.4260 


0.3820 


0.3400 


0.3020 


0.2680 


0.2380 


0.2I2o'o. I9O0' O.I7OO 


0. 1500 0. 1380 


2 


0.2990 


0.2610 


0.2320 


0.2080 


0.1860 


0.1660 


0.1500 


0.1340 


O.I2IO 


O.IO90 O.O99O 


. 0890 


0.0800 


3 


0.2107 


0.1853 


0.1660 


0.1487 


o.i333 


0.1200 


0.1080 


0.0980 


O.0880 


O.0800 O.O733 


0.0675 


0.0600 


4 


0.1670 


0.1465 


0.1310 


0.1175 


0.1060 


0.0960 


0.0870 


0.0795 


O.O725 


O.0665 O.0605 


0.0550 


0.4495 


5 


0.1400 


0.1232 


0.1 104 


0.0966 


0900 


0.0816 


0.0740 


0.0676 


O.062O 


O.O592J0.O52O 


0.0476 


0.0436 


6 


0.1217 


0.1067 


. 0960 


0.0870 


0.0787 


0.0717 


0.0653 


0.0597 


O.O550 


O.O5O3 O.O463 


0.0427 


. 0390 


7 


0.1089 


. 0949 


0.0847 


0.0774 


0.0706 


0.0643 


0.0588 


. 0540 


O.O497 


0.0460! O.O423 


0.0388 


. 0360 


8 


0.0978 


0.0858 


0.0775 


0.0705 


. 0642 


0.0585 


. 0540 


0.0498 


O.O458 


O.O423 O.O39O 


0.0359 


0.0335 


9 


0900 


0.0791 


0.0715 


0.0651 


0.0593 


0.0544 


0.0500 


. 0460 


O.O427 


O.O395 O.O367 


0.0340 


0.0316 


10 


0.0836 


0.0732 


0.0666 


0.0606 


o-o554 


0.0508 


0.0468 


0.0434 


O . 0402 


O.O372O. O348 


0.0324 


0.0302 


11 


0.0782 


0.0687 


0.0624 


0.0571 


0.0524 


0.0482 


0.0445 


0.041 1 


O.O384 


O.O356 O.O33O 


0.0311 


0.0289 


12 


0.0735 0.0648 


0.0592 


0.0542 


. 0498 


0.0458 


0.0423 


0390 


O.O365 


O.O34O O.O315 


0.0297 


0.0277 


13 


0.06950. 0615 


0.0561 


0.0515 


0.0474 


0.0437 


. 0405 


0.0375 


O.O349 


0.0328^.0306 


0.0285 


0.0266 


14 


0.06630 0586 


0.0533 


0.0491 


0.0451 


0.0419 


0.0389 


0.0361 


O.O337 


O.O317 


O.O296 


0.0263 


0.0259 


15 


0.0633 0.0561 


0.0513 


0.0475 


0.0435 


. 0403 


0.0375 


0.0349 


O.O325 


O.O3O5 


O.O280 


0.0268 


0.0257 


16 


0.0608 0.0540 


0.0494 


0.0455 


0.0420 


0.0390 


0.0363 


0.0338 


O.O316 


O.O295 


O.O278 


0.0261 0.0244 


17 


0.0582 0.0520 


0.0477 


0.0441 


0407 


0.0378 


0.0353 


0.0328 


O . O308 


O.O289 


O.O272 


0.0255 0.0240 


18 


0.0564 0.0504 


0.0462 


0.0426 


0.0396 


0.0364 


0.0342 


0.0321 


O.O30I 


O.O282 


O.O264 


0.0250 0.0235 


19 


0.05450 0487 


0.0448 


0.0414 


0.0384 


0.0358 


0.0335 


0.0314 


O.O295 


O.0278 


O.O262 


0.0245 °-° 2 33 


20 


0.0528 0.0473 


0.0435 


0.0403 


0.0375 


0.0349 


0.0327 


0.0307 


O.O289 


O.O273 


O.O257 


0.0241 0227 


21 


o.05io'o.o46o 


0.0424 


0.0394 


0.0364 


0.0342 


0.0320 


. 0302 


O.0284 


O.O268 


O.O252 


0238 0.0224 


22 


0.0496 0.0450 


0.0414 


0.0384 


0.0358 


0.0334 


0.0314 


0.0296 


O.0280 


O.O264 


O.O248 


0.0234 0.0220 


23 


0.04830. 04 39 


0.0404 


0.0374 


0.0350 


0.0327 


. 0308 


0.0290 


O.O274 


O.O258 


O.O244 


0.0230 0.0216 


24 


0.0471 0.0436 


0.0396 


0.0368 


0.0342 


0.0320 


. 0302 


0.0285 


O.O269 


O.O254 


O.O24I 


0.0229 0.0213 


25 


0.0460 0.0418 


0.0386 


0.0360 


0.0336 


0.0314 


0.0256 


0.0279 


O.O265 


O.O250 


O.O236 


0.0226 0.0210 


26 


0.0448 0.0408 


0.0378 


0.0352 


0.0328 


0.0308 


0.0290 


0.0274 


O.O260 


O.O246 


O.O233 


0.0221 0.0208 


27 


0.0439 0.0400 


0.0370 


0.0346 


0.0322 


0.0302 


0.0286 


0.0270 


O.0256 


O.O243 


O.O23O 


0.0218 0.0206 


28 


0.0430 0.0392 


0.0364 


0.0340 


0.0318 


0.0298 


0.0282 


0.0266 


O.O252 


O.O24O 


O.O228 


0.0216 0.0204 


29 


0.0421 0386 


0.0358 


0.0334 


0.0313 


0.0294 


0.0277 


0.0263 


O.O25O 


O.O237 


0.0225 


0.0213 0.0201 


30 


0.04130. 0378 


0.0352 


0.0328 


0.0307 


0.0289 


0.0273 


0.0259 


O.0246 


O.O234 


0.0222 


0.0210 0.0199 


3i 


0.0404 0.0371 


0.0347 


0.0323 


0.0304 


0.0284 


0.0268 


0.0255 


O.O243 


O.O23I 


O.O219 


0.0208 0.0197 


32 


0.0397 0.0364 


0.0339 


0.0318 


0.0298 


0.0281 


0.0265 


0.0252 


O O24O 


0.0228 


0.02l6 


0.0205 0.0195 


33 


0.0390 0.0358 


0.0335 


0.0313 


0.0294 


0.0277 


0.0262 


0.0249 


O.0237 


0.0226 


O.O2I4 


0.0203 0.0193 


34 


0.0382 0.0353 


0.0330 


0.0309 


0.0290 


0.0274 


0.0260 


0.0246 


O.O235 


O.O224 


0.02I3 


0.0202 0.0191 


35 


0.0376 0.0347 


0.0325 


0.0304 


0.0286 


0.0270 


0.0256 


0243 


O.023I 


0.0220 


0.02IO 


0.0200 0.0190 


36 


0.0370 0.0342 


0.0320 


0.0300 


0.0283 


0.0267 


0.0254 


0.0244 


O.023O 


O.O219 


O 0208 


0.0198 0.0188 


37 


0.0364 0.0336 


0.0315 


0.0297 


0.0279 


0.0264 


0.0251 


0.0239 


0.0228 


O.O217 


0.0206 


0.0196 0.0186 


38 


0.0358 0.0332 


0.0312 


0.0293 


0.0276 


0.0262 


0.0248 


0.0235 


0.0226 


0.02I5 


0.0205 


0.0195 0.0185 


39 


0.0353 0.0328 


0.0308 


0.0290 


0.0274 


0258 


0.0246 


0.0234 


0.0223 


0.02I3 


0.0203 


0.0193 OI 83 


40 


0.0349 0.0323 


0.0303 


0.0289 


0.0271 


0.0256 


0.0243 


0.0232 


0.022I 


0.02II 


0.020I 


0.0191 0.0181 



The fact that the coefficient of friction varies greatly with 
change of pressure is here exhibited with no less certainty. It 
is also seen that the method of variation varies somewhat with 
different lubricants, in some cases varying very nearly in- 
versely with the intensity of pressure, and the total frictional 
resistance remaining nearly constant within wide limits of 
alteration of pressure. It is here found, as in the experiments 



FRICTION OF L UBRICA TED S URFA CES. 3 39 

of the Author, that the increase of speed raises the pressure 
per unit of area attainable, and that the speed giving minimum 
friction rises with increasing pressure. 

The journals in the cases here cited were so arranged that 
the pressure was unintermitted. It remains to be determined 
how intermission of pressure modifies the laws affecting fric- 
tion. It is only known, as yet, that it permits the use of 
much higher pressures — sometimes double those safely used in 
the former case. 

Some of the most important conclusions which have been 
deduced from the later experiments described above were 
anticipated by Mons. G. A. Him,* who found by experi- 
ment, about 1855, tnat a lubricant gives least friction after 
working some time; that friction is diminished by increase of 
temperature ; that, under favorable conditions of lubrication, 
friction increases in ordinary cases as velocity increases ; and 
that the resistance is proportional to the square root of the 
product of area and pressure ; i.e., the coefficient varies in- 
versely as the square root of the pressure — a conclusion later 
confirmed by the Author. 

144. Fluid Pressure and Friction are here controlling 
conditions. The former evidently in some cases, as seen above, 
more than mere capillarity, sustains the load, and holds the 
two surfaces out of contact ; the latter produces the observed 
resistance. The intensity of this pressure was found to be, in 
experiments already cited, sometimes more than 200 lbs. 
per square inch (14 kgs. per sq. cm.) when the average load 
on the journal was one half that amount. In cases such as 
this, in which no oil-grooves are made in the bearing or in the 
cap to which the oil-cup is attached, difficulty is often found 
in securing a free feed of the oil. In nearly all cases the en- 
gineer cuts small channels or " oil-grooves" from the oil-hole 
across or diagonally, or in both directions, to the further por- 
tions of the " brass," and thus succeeds in supplying them with 
oil. Those " reservoir-boxes" in which the oil-bath is incor- 
porated give the best adjustment of fluid-pressure. 

* Introduction a la Mecanique Industrielle; Poncelet. 



340 FRICTION AND LOST WORK. 

145. Conclusions.*— Specified Qualities may, by the pro- 
cesses here described, be secured by the identification by test 
of a lubricant possessing such properties. If an unguent is 
desired for heavy pressures, or an oil for very light work, or 
for high or low speeds of rubbing under known pressures, the 
methods of study of the available lubricants which have been 
described will enable the engineer or the manufacturer to 
select that which is best suited to the specified purpose. He 
may go still further, and, by repeated mixing and test gradu- 
ally improve the mixtures, may finally secure compounds 
having the best possible qualities for the various proposed 
applications. The Author has in this manner sometimes 
produced lubricants for manufacturers which have been found 
peculiarly well suited for special lines of trade. 

Studying the facts here stated, and the data acquired by 
many hundreds of other experiments, made on one or the other 
of these last-described machines for testing lubricants, we may 
recapitulate the facts and figures for ordinary use in machine- 
design and in estimating losses of power by friction as follows : 

(1) The great cause of variation with well-cared-for journals, 
since they must work at ordinary temperatures, is alteration 
of pressure and variation in methods of supply ; and it is seen 
that the higher pressures give the lowest percentages of loss 
of power by friction. 

(2) The value of the coefficient is greatly modified by the 
state of the rubbing surfaces ; a single scratch has its effect in 
wasting power. A good journal usually has its surface as 
smooth and as absolutely uniform as a mirror. Every well- 
kept journal acquires such a surface. 

(3) For general purposes and for heavy work, as in the ex- 
periments of the Author, and at considerable speeds, the value 
of the coefficient varies nearly inversely as the square root 
of the pressure, for pressures ranging from 50 to 500 lbs. per 
square inch. 

(4) The coefficient for rest or starting may similarly be 



* See Trans. Am. Inst. Mining Engineers, 1878; Journal Franklin Institute, 
November, 1878. 






FRICTION OF LUBRICATED SURFACES. 34 1 

taken to vary nearly as the cube root of the pressure. For 
closer estimates and other conditions, the tables just given can 
be referred to directly. 

(5) The coefficient for the instant of coming to rest, under 
the special conditions here referred to, is nearly constant, and 
may be taken at 0.03. 

(6) The resistance due to friction varies with velocity, de- 
creasing with increasing velocity rapidly at very low speeds, as 
from 1 to 10 feet per second, and slowly as higher speeds are 
reached, until the law changes and increase at ordinary tem- 
peratures takes place, and at a low rate throughout the whole 
range of usual velocities of rubbing met with in machinery. 

Its amount and the law vary with method of lubrication, 
however. With oil-bath lubrication the value of f usually 
varies more nearly as the square root of the velocity. 

(7) With pressure and velocity varying, we may take the 
coefficient as varying as the fifth root of the velocity, divided 
by the square root of the pressure for such work as is repre- 
sented by the experiments of the Author. 

(8) The effect of heating journals under conditions here 
illustrated is, to increase the friction above 90 or ioo° F., at a 
speed as low as 30 to 100 feet per minute, while at higher 
speeds and low pressures the opposite effect is produced, and 
the coefficient often decreases more nearly as the square root 
of the rise of temperature. 

(9) The temperature of minimum friction, under the con- 
ditions of the experiments here referred to, varies nearly as 
the cube root of the velocity, for a pressure of about 200 
lbs. per square inch. 

(10) The endurance of any lubricant should be determined 
by actual wear upon a good journal under the pressures and 
velocities proposed for its use. 

The economy with which it can be used will be dependent 
upon its natural method and rate of flow, and upon its capillary 
qualities, as well as upon its intrinsic wearing power and the 
method adopted in feeding it. Greases, therefore, are usually 
more economical in cost than oils, even if having less wearing 
capacity. 



34 2 FRICTION AND LOST WORK. 

(u) The only method of learning the true value of a lubri- 
cant and its applicability in the arts is to place it under test, 
determining its friction-reducing power, and its other valuable 
qualities, not only at a standard pressure and velocity, and at 
ordinary temperatures, but measuring its friction and endur- 
ance as affected by changing temperatures, speeds, pressures, 
and methods of application, throughout the whole range of 
usual practice. 

(12) The true value of an oil to the consumer is not pro- 
portional simply to its friction-reducing power and endurance, 
under the conditions of his work ; but its value to him is 
measured by the difference in value of power expended, when 
using the different lubricants, less the difference in total cost 
of oil or grease used; but for commercial purposes, no better 
method of grading prices seems practicable than that which 
makes their market value proportional to their endurance, 
divided by their coefficients of friction. 

The consumer will usually find it economical to use that 
lubricant which is shown to be the best for his special case, 
with little regard to price, and often finds real economy in 
using the better material, gaining sufficient to repay excess in 
the total cost very many times over. 

(13) To secure maximum economy, the journal should be 
subjected to a pressure the limit of which is determinable by 
either Rankine's or Thurston's formula (Art. 127); the most 
efficient materials should be chosen for the rubbing surfaces ; 
they should be reduced to the most perfect state of smoothness 
and perfection in form and fit ; a lubricant should be chosen 
which is best adapted for use under the precise conditions 
assumed ; the lubricant should be supplied precisely as needed, 
and by a method perfectly adapted to the special unguent 
chosen. The real problem is often not what oil shall be used, 
but how to secure most effective lubrication. 

(14) The semi-fluid lubricants, when equally good reducers 
of friction, are usually the most economical for heating jour- 
nals, in consequence of their peculiar self-regulating flow, as 
the rubbing parts warm or cool while working. They are 
usually too viscous for economical use in ordinary work. 






CHAPTER VIII. 

THE FINANCE OF LOST WORK AND THE VALUATION OF 

LUBRICANTS. 

146. The Conditions affecting Values, both of the lost 
work produced by friction and of the unguent used in reducing 
its amount, have been already stated (Art. 51, Chap. III.) to in- 
volve other and far more important considerations than the 
market-price of the lubricant. The principles involved were 
stated by the author in an earlier work ;* the treatment to be 
here given is a more complete development of the subject. 
Demand usually, if sufficient time is allowed for its operation, 
brings prices into a correct relative order, but not necessarily 
into a true proportion of values for any one specific applica- 
tion. It is generally the fact that " the best is the cheapest" 
to the consumer, and this rule is probably almost always appli- 
cable in the purchase and use of lubricants. It is frequently 
the fact that the consumer can better afford to use the highest- 
priced article than to take those of lower value as a gift. 

A very roughly approximate value by which to compare 
the oils can be sometimes based on the assumption that they 
will have a money-value proportionate to their durability and 
to the inverse ratio of the value of the coefficient of friction. 
Thus : Suppose two oils to run, one 10 minutes and the other 
5, under a pressure of 100 lbs. per square inch, and both at 
the same speed, and suppose them to give on test for friction 
the coefficients 0.10 and 0.06 respectively. 

Their relative values might be taken at -J-jj- = 1 and -jj- = 0.833. 
If the first is worth one dollar the second should be worth 83-g- 
cents. 

* Friction and Lubrication. R. H. Thurston, New York, Railroad Gazette 
Pub. Co., 1879. 



344 FRICTION AND LOST WORK. 

In many cases, however, about the same quantity would 
be applied by the oiler, whatever oil might be used, and their 
values to the consumer would be taken in the inverse propor- 
tion of the values of their coefficients of friction, i.e., as, in the 
above case, 6 is to 10, thus making the value of the second 
$i.66f, and showing that it would be better to use the latter 
at anything less than this price than the first at one dollar. 

Engineers have been accustomed to use these methods of 
comparison in reporting upon the values of lubricants simply 
because they are generally considered to be correct by dealers 
and users, and because there has been no better method sug- 
gested of assigning an approximate figure for market price. 

The real difference in values of any lubricants, to any user, 
may, nevertheless, be determined in any given case when 
the cost of power is exactly known, and when the quantity 
of the several unguents required to do the same work has 
been found, and their several coefficients of friction given. 
The difference in actual value to the user, where any two 
unguents are compared, is measured by the difference in the 
costs of power and other expenses expended in driving the 
machinery when lubricated first with the one and then with 
the other of the two materials. As power is usually much 
more expensive when developed in small, than when demanded 
in large, amounts, the economy to be secured by adopting a 
good lubricant is the greater as the magnitude of the work is 
less. In large mills, and wherever work is done on a very large 
scale, the cost per horse-power and per annum may be taken 
roughly at about $50 a year, while for small powers this figure 
is doubled or even trebled and quadrupled. 

Every reduction of power to the extent of one horse-power, 
by the introduction of an improved material or system of lubri- 
cation, thus effects a saving of $50 to $100 a year; the differ- 
ence between this amount and the extra cost of the new kind 
of lubricant represents the annual profit made by the change. 
Should it happen, as is sometimes the fact, that the better 
unguent is also the cheaper, an additional profit is made which 
is measured by that saving in cost. 

In an ordinary small mill or in a machine-shop in which 100 



THE FINANCE OF LOST WORK. 345 

horse-power is used, a change in lubricant will often effect an 
average saving of 5 horse-power and a consequent economy of, 
probably, $500 a year. The total amount of oil used in such 
a case might considerably exceed 100 gallons. 

The consumer could in such a case better afford to pay $5, 
or perhaps even more, per gallon for the good oil than accept 
the less valuable lubricant as a gift. 

In mills filled with light machinery, where the mean value 
of the coefficient of friction is greater, and where a larger pro- 
portion of the total power expended is used in overcoming the 
friction of lubricated parts, a saving of 15 or 20 per cent, has 
been made by the substitution of a good oil for a worse, i.e., a 
gain of 75 to 100 horse-power on 500, and of $3000 to $5000 
per annum in power alone. In a case reported by Mr. Comfy,* 
a reduction of cost of oil on a single engine from 3.53 to 0.78 
cents per hour was effected by the use of a slowly-flowing 
grease instead of a freely-flowing oil. The cost of lubrication 
of shafting was similarly reduced 44 per cent., but the loss by 
increased friction was not noted. An instance is reported by 
Mr. Woodburyf in which a gain of power of 33 per cent, was 
effected by change of grease for a light oil, the loss in cost of 
lubricant becoming comparatively unimportant ; in still another 
instance the production of a mill was thus increased 5 per 
cent., while also greatly reducing the lost work of friction. 

This subject is of such importance, and has as yet received 
so little attention, that it has been considered advisable to de- 
vote a chapter to its development. 

The differences in value of good oils, and the enormous 
wastes of power, and of other costs, with unguents of poor 
quality, are easily exhibited. Assuming the cost of a good oil 
at $1 per horse-power per annum, in any case, a variation of 
one per cent, in the coefficient of friction produced by a change 
of oil will produce a gain or loss of from 50 to 100 per cent, 
of the total cost of oil used in the shop or mill, and of 
other costs of power accordingly as the mean coefficient is 
high, as in cotton and other mills filled with light mechanism, 

* Trans. Am. Soc. M. E., 1884. f Ibid. 



34-6 FRICTION AND LOST WORK. 

or low as in the locomotive engine and other heavy machinery. 
The use of good instead of bad, or of an oil with low " cold- 
test" in winter instead of one easily stiffened by low tempera- 
ture, may enable an engine to haul two or three additional 
cars in a train, or a mill to be driven easily and economically, 
where otherwise it could not be driven, if at all, by an engine 
of proper proportions except very wastefully. 

The use of a poor quality of cylinder-oil will sometimes 
cause losses by increased friction of engine, and even on loco- 
motives by breakage of rods and rock-shafts, sufficient to com- 
pensate many times over the gain in money cost of oil. Under 
heavy pressures, also, the cost of wear and tear of journals and 
bearings may become a serious item. 

All lubricants should be purchased with careful regard to 
their value, rather than by reference mainly to their price. 
Their value is determined principally by their friction-reducing- 
power, and their reduction of wear of rubbing parts. Unguents 
of low grade cause losses, direct and indirect, which are out of 
all proportion to their low cost, and may invariably be expected 
to produce such losses by waste of power, by injury to jour- 
nals and bearings, and by destruction of valuable machinery,, 
to say nothing of the dangers of fire which often accompany 
their introduction, that the user can generally better afford to 
pay many times their value for the privilege of declining to 
use them, than to submit to the enormous losses sure to follow 
their application to his machinery. In every case the lubri- 
cant should be carefully selected for the special use intended. 

147. The Defects in the Usual Methods of valuation of 
lost work and of lubricants are readily seen to arise from the 
fact that they include simply a comparison of the market- 
price of available kinds and qualities with their endurance and 
friction-reducing power. It is usually assumed that, of two oils 
having endurance and friction-coefficients in the inverse ratio 
of their prices, the purchaser may take either with practically 
equally good financial result. No comparison is usually made 
of the relative costs of wasted power and of total expense for 
oil. This system is obviously entirely wrong, as is every 
method which does not take into account every item of profit 



THE FINANCE OF LOST WORK. 347 

and loss variable with change in quality and quantity of lubri- 
cant, and which does not make up an account including all 
these items. The real question is not whether the difference 
in price of any two oils is justified by the difference in their 
intrinsic qualities, but whether the profit or loss to be made by 
the substitution of one for the other is compensated by the 
total loss or gain in expense. 

148. An Exact Method of valuation of lost work and of 
lubricants must include a determination of the intrinsic quali- 
ties of the latter, their influence upon the magnitude of the 
former, and of the money-value of every item of gain and loss 
in the purchase of the lubricants, in the variation of the quan- 
tity of power used, and in all incidental expenses, such as wear 
and repairs, taxes, insurance, rents, availability of the property, 
and many other items that may be usually determined in any 
given case. An expression must be obtained for the total of 
all these costs of wasted power and of lubricant for the actual 
and for the proposed case, and a comparison of the amounts 
so determined will indicate the magnitude of the gain or loss 
to be produced by the proposed change. 

149. The Theory of the Finance of Lost Work includes 
a comparison of economy in the use of various lubricants, which 
is evidently not that of the relative cost of operation with and 
without lubricants, but of the relative total costs of working 
with two or more available unguents. The costs include the 
expense of the lubricant and of repairs, and the value of the 
work wasted by friction in the several cases. 

If the cost of the lubricant per unit of quantity is k, and 
if the quantity used in the assumed time be q, the cost of the 
lubricant is kq. If the amount of work lost by friction in the 
given time be U, and if its total cost be k' per unit of work, 
and for the assumed time, the expense chargeable to lost work 
is k'U\ while the total expense due to friction of the apparatus 
is, neglecting other expenses as unimportant, 

K=kq^-k'U. (1) 

But the work is 

U = a/PS = afPVt, (2) 



34 8 FRICTION AND LOST WORK. 

the product of the coefficient of friction,/", the total load, P, 
the mean velocity of rubbing, V, the time, t y and a constant, a, 
dependent upon the relations assumed for space and time ; 
hence, 

K= kq + k'afPS. (3) 

For any given cases taken for comparison, the only vari- 
ables in the second member of the above equation are q and/, 
and, making ak'PS =b, 

K=kq + bf; (4) 

in which b is determinable for each case of comparison. That 
lubricant which gives the least value of K is best. The true 
value of a proposed oil will vary as 

'T±* » 

The above equations show that the value of the lubricant is 
inversely as the quantity required, and, when the cost of un- 
guent is small in comparison with the value of the lost work or 
wasted power, its commercial value, which varies with the de- 
crease effected in K, is directly as some function of its lubri- 
cating power, i.e., nearly as the reciprocal of the coefficient of 
friction. If the cost of oil is large, the comparison becomes 
one of the expense for lubricants. 

Two oils being compared, the costs of lost work are, re- 
spectively, 

K x = Kq x + b/ x >, K = to + &,\ 

and the saving effected by the substitution of a better lubri- 
cant is 

K.-K^k^-k^ + b {/,-/,). ... (6) 
When K x = K v (6) becomes zero, and since 



THE FINANCE OF LOST WORK. 349 

the changeis a matter of in difference ; if K x — K 2 is greater, 
the change is advisable, otherwise it is not ; and where K x = 
K„ the gain by lower cost of oil is just compensated by in- 
creased loss of power. Thus the equation 

Kq* - Kq, = &{A — /.), 

22 

is the criterion determining advisability of making a change of 
lubricant. A higher cost for the proposed oil than k x would 
be uneconomical. 

It is very often the fact that the quantity of the oil used 
has little connection with the behavior of the journal upon 
which it is used, and q x may be taken equal to q v when the 
expression becomes the condition of economy, and the criterion 
is given by 

K=i,= 6 -(A -/,) + *. (8) 

21 

Where the effects of using different quantities of the same 
oil are compared, k x = k„ and the criterion is 

ft=.|(/-X) + ^; (9) 

i 

the use of any quantity less than q 2 is an advantage. As the 
friction of lubricated surfaces is sometimes enormously affected 
by the freedom of supply of the unguent, the consideration of 
this case is very important. The lower the price of the lubri- 
cant, and the higher the value of the power, the more freely 
may the oil be supplied. 

In all such cases, therefore, we have the cost of wasted 
power a function of q x , and when, as is always the fact in prac- 
tice, the law connecting the variation of K with the variation 
of q can be ascertained, exactly or approximately, by experi- 
ment, and can be expressed by an algebraic equation, the most 



350 FRICTION AND LOST WORK. 

economical rate of supply, i.e., the best value of q v may be de- 
termined by making 

dK __ 
dq 
for a minimum.* 

When the relative durability and the coefficients of friction 
are known, as determined by experiments made under the ex- 
act conditions of intended use, it becomes easy to determine 
their relative values. Taking that actually in use as the 
standard, if the proposed lubricant be found to have e times 

the endurance of the standard, the quantity used will beq 2 = - 

If the second oil also have a coefficient of friction h times as 
great as the first, the work of friction will be correspondingly 
decreased or increased, and the cost of that work will be bhf v 
The total costs thus become 

K x = Kq x + bf x ', (10) 

K, = i*+'MA; ..... (ii) 

and the criterion of economy is given by making K x = K„ and 

K = K= e - [fa, + bf, (i - h)\ . . (i2) 

A higher cost causes loss, a lower is a gain ; this value of k 
being that which the buyer can pay for the lubricant in place, 
on the journal, without losing by the change. 

It is obvious that b may be expressed in any units of cost 
that may be convenient, as on railroads, in repairs, fuel, or other 
material expended per train-mile. Thus on railroads the ex- 
penses of hauling trains are measured by the costs of oil, re- 
pairs, and of power per train-mile, and 

K=kq + df, (13) 

* See Friction and Lubrication; also, Encyclopedia Britannica, art. "Lubri- 
cants." 



THE FINANCE OF LOST WORK. 351 

in which q is the quantity of oil used and df is the cost of 
power and attendant expenses per train-mile. This makes 
the criterion 

Kq, -Kq, = d (/ -/ 2 ); 

v=^ ^fy.-A . . ( I4 ) 

Where, as may often occur, the reduction of friction is ac- 
companied by increased expenses on account of wear of journals 
and bearings, a third term must be introduced and the varia- 
tion of the total thus obtained noted. For ordinary pressures, 
in well-designed mechanism, the last item may probably be 
neglected ; but in some cases, as in transportation on railways, 
it may become, and probably often is, a very serious item of 
expense, and must be taken into account. 

150. Data required in Applying the Theory, although 
usually obtainable with satisfactory exactness in any given 
case, are not sufficiently uniform to permit their statement in 
figures for general use. 

The total expense chargeable to lost work in machinery 
consists of the following items : 

(1) Cost of power produced, only to be wasted, including 
all items of cost in the motive-power department. 

(2) Expense incurred by " wear and tear" of the driven 
machinery and its repair and replacement. 

(3) Indirect, casual, and remote money-losses due to in- 
efficiency caused by friction and by wear. 

(4) Cost of lubricants and of their application. 

The first item includes all running expenses of the motor, 
including fuel and supplies, interest on invested capital, wages, 
insurance, and taxes on the engine, boilers, and buildings 
covering them. The second, which is a large item, includes 
the replacement of worn bearings and journals, and parts in- 
cluded in their depreciation, sometimes the latter involving 
finally the whole machine. In fact this is the usual limit of 
the life of the machine. The third item cannot be calculated, 
since it includes accidents, but it may usually be covered, like 



35 2 FRICTION AND LOST WORK. 

other casualties, by a system of insurance. The fourth item is 
the least important of all. It includes the purchase of the 
lubricant, its transportation, and the expense of its application 
and removal and of keeping the bearings clean. Although the 
smallest of these expenses, this is most obvious to the con- 
sumer, and is wrongly allowed to determine, usually, the selec- 
tion of the unguent. A change of lubricant usually effects 
enormous changes in the magnitudes of the first three items, 
and comparatively insignificant alterations of cost in the last. 
As the total resistance is composed partly of friction of fluids, 
and partly of that of solids, some lubricants are found to give 
reduced resistance, while nevertheless increasing wear inordi- 
nately. In such cases, the lubricant is found to have too small 
viscosity, and the decreased fluid resistance, although not com- 
pensated by increase of solid friction, is more than counter- 
balanced in the expense account by cost of increased wear. 

151. The Units of Measurement to be adopted in the 
commercial theory of lost work will be determined by circum- 
stances. As a rule, the cost of power is measured in dollars or 
cents per horse-power, or per foot-pound, per hour of working 
time, which is usually about three thousand hours per annum. 
The usual charge for the horse-power in New York City, for 
example, in small amounts, is $100 per annum, equivalent to 
$0,033 P er hour. The cost of wear and tear and of deprecia- 
tion is very variable, but can be best estimated as a percentage 
of the value of the machinery; 2-J- per cent, for renewals and 
something more for minor repairs is a common figure. All taxes 
and insurances are reckoned by a similar method. The cost of 
lubricants may be reckoned from the quantity used per hour. 

All expenses being thus reduced to one measure — money- 
cost — it becomes easy to solve any problem of this kind aris- 
ing in practice when the requisite data are obtainable. 

The costs are thus made to appear finally as two items — 
the one the cost of the lubricant, and the other that of the 
wasted power — which are regarded as independent variables, 
although evidently dependent according to some law which 
may possibly be sometimes easily expressed. The data re- 
quired are often exceedingly difficult of determination, and 






THE FINANCE OF LOST WORK. 353 

approximate results only can be reached. This is especially 
true of cost of wear and repairs. 

152. The Values of Quantities entering the preceding 
theory are often ascertainable : they are mainly costs of 
power, of oils, and of depreciation. The cost of power will 
vary according to amount, efficiency of engine, costs of wages, 
fuel, and minor items, from $40 per annum, or $0,013 per 
hour, to $200 per year, or $0.07 per hour, nearly : the higher 
figures being for very small, and the lower costs for large and 
economical condensing engines, with cheap fuel and labor. 
The mean may be assumed as $60, or $0.02 per hour, for good 
non-condensing, stationary engines of 100 to 200 horse-power. 

This annual expense is divided, in some cases noted by the 
Author, thus : 

Total. Coal and Oil. Wages. Minor Costs. 

Small engines $200 $50 $100 $50 

Medium " 60 25 25 10 

Large " 40 20 10 10 

In marine work, the cost of fuel often becomes a larger per- 
centage of the total ; perhaps 60 to 80 per cent, may be con- 
sidered a common allowance. 

The power demanded for overcoming friction of engine 
and shafting of mills may be taken at from 0.20 of the total on 
heavy work, to 0.30 on light, the total power ranging from 10 
to 20 horse-power, averaging 15, per 1000 spindles and " pre- 
paration." 

The cost of oils in the market has no direct relation to 
their values as lubricants, and is not infrequently in the inverse 
order, the best costing least, and the most expensive having 
a comparatively low position as unguents for the specific pur- 
pose considered. Taking them as they come, however, the 
following may, for purposes of illustration, be assumed to be 
fair relative values : 

Sperm-oil, per gallon $1 10 

Neat's foot oil, per gallon 1 00 

Lard-oil, " " o 70 

Tallow-oil, " " , o 70 

Olive-oil, " " 090 



354 FRICTION AND LOST WORK. 

Cotton-seed oil, per gallon o 50 

Greases, per pound o 25 

Mineral oil, heavy and fine o 80 

fair o 50 

light 040 

spindle, light o 30 

natural W. Va o 25 

kerosene o 10 

The quantity used will vary greatly with its use and the 
method of application. Cotton- mills use from 10 to 30 
gallons per 10,000 lbs. of cloth made, or about 10 gallons 
per annum per horse-power, at a cost averaging $0.70 to $1.00 
per gallon. A mill of 60,000 spindles, making 3,000,000 
lbs. of cloth per year, and demanding 1200 horse -power, 
uses about $2000 worth of oil. The cost of replacement of 
wearing parts is small. Railway-engines use 0.005 to °- 01 
gallon per " train-mile," and 40 to 60 lbs. of coal. Cylinder 
oils are used in the proportion of from 200 to 600 miles run 
per gallon. 

The ordinary passenger locomotive on New England rail- 
roads averages an expenditure of between 60 and 70 lbs, of coal 
per mile, at a cost of not far from 15 cents; while an expense of 
one half cent per mile for oil and tallow is considered a good 
showing. A run of 30 miles per ton of coal and of 100 miles 
per gallon of oil is not an unusual figure on Western roads. The 
cost of fuel is often about one third the total cost per mile ;, 
that of oil about two or three per cent of the total. Two or 
three times as much oil is used under a passenger car as under 
a freight car. The cost of repairs is enormously variable. It 
has been found in some cases of good practice that a pound of 
bearing and a pound of journal are worn away by, respectively, 
twenty-five thousand and seventy-five thousand miles of travel. 
But the cost of this form of depreciation alone is enormously 
greater than the mere cost of material per pound. Using a 
black oil, the cost of wear has been found five times that of the 
lubricant and twice that of power. 

A large machine-shop is reported to have used one thou- 
sand tons of coal per annum for all purposes, including heating, 
to demand 120 horse-power from its engines, and to use 450 



THE FINANCE OF LOST WORK. 355 

gallons of oil, the cost being $6500 for coal and $250 for oil. 

Another moderately large shop uses but 60 gallons of oil per 

year, or about 0.02 gallons per hour of working time. The 

cost of wear should be insignificant. 

153. Illustrations of Application may be taken as below : 
Calling the total value of the horse-power $100 per annum, 

or $0.03 per hour, the value of b will be found as a function of 

k'afPS. The value of k' will be 



k' = '° 3 



1,980,000 

if a is taken as unity, i.e., one hour, and 

b — 0.000,000,015 /PS. 

Assume PS = 4,000,000,000 a fair figure for an iron-work- 
ing establishment wasting 100 horse-power in friction. Then 
b = $60 = 0.6 H. P. ; and if in equation (4)/= 0.05, k x = $0.50, 
and q x = 0.02 gallon per hour, 

Ki — Klx + ^/i — °- 01 + 3-°° — $3-oi. 
Assume k 2 = $0.25 ; q 2 = 0.03 ; /= 0.06 ; then 
K % = Kq % + b/ = 0.0075 + 3.6o = $3-6of ; 
K, — K 7 = — $0.60 nearly. 

The cost of lost power is increased 20 per cent, and $0.60 
per hour is lost by a saving of one quarter of a cent per hour 
in cost of lubricant by the substitution of an oil giving a coefrl- 
cient of 6 per cent., and demanding one half more oil for a 
lubricant giving a mean coefficient of 5 per cent. The saving 
in cost of oil is insignificant; the loss in cost of power is com- 
paratively enormous ; although the difference in the coefficient 
is but one per cent. 

If by freer supply of the cheaper oil, as by the oil-bath, the 






356 FRICTION AND LOST WORK.. 



value of f x can be reduced, as is not unlikely, to/i = 0.02, if 
q x = 0.40 and k = 0.25, we get 

K\ = 0.10+ 1.20 = $1.30; 

K - K\ = $2.30 ; k# % - k\q\ = $0.0925 ; 

and the expenditure of nine cents per hour for additional oil 
produces per hour a gain of $2.30, i.e., a profit of about 2500 
per cent. 

If one oil gives a mean coefficient of friction, /^ = 0.05 and 
another / 2 = 0.06, using 0.02 gallon per hour of each, the real 
value of the latter becomes (Eq. 7) 

= 0.01+60(0.05-0.06) = _ 

2 0.20 yj 

and the proprietor will do well to pay $3.05 per gallon for the 
privilege of declining its use ; since, if it is used, he loses that 
amount on every gallon. 

If a low-grade oil be in use at k^ = $0.25 per gallon, giv- 
ing f 2 = 0.06 when using q 2 = 0.2 gallon per hour, it will pay 
to substitute the higher quality at any cost not exceeding, per 
gallon, 

= 0.05 +.60(0.06-0.05) 

0.20 ° D 

which exceeds several times the cost of the most valuable oils 
used for lubrication. 

In fact, as is evident, the importance of reduction of the 
cost of unguent is usually absolutely insignificant in compari- 
son with that of securing the best possible lubrication. The 
fact is also here made evident, that no system of determination 
of the relative value of lubricants can give more definite results 
than that of applying the steam-engine " indicator" to the 
driving-engine, and using the oils to be compared one after 
another, and long enough to eliminate the effect of each upon 
that which follows it. 



THE FINANCE OF LOST WORK. 357 

The following is a still more striking case : Assume a cot- 
ton-mill to contain machinery demanding 400 horse-power to 
overcome friction, to use one fifth of a gallon of oil per hour, 
averaging one dollar per gallon, and giving a mean coefficient 
of friction of f x — 0.10, and the total cost of power to amount 
to $60 per horse-power per year of 3000 working hours. Then 
b — 80, and 

K 1 — 0.20 X 1.00 + So X 0.10 = $8.20 per hour. 

If a change of oil is made, and k 2 = 0.25, q 2 = 0.3, and 
y* 2 = 0.15, as may readily occur, the cost per hour is 

K 2 = 0.25 x 0.3 + 80 x 0.15 = $12,074, 

and a gain of 65 per cent, in cost of oil causes a loss of about 
50 per cent, in cost of wasted power ; or $375 gain per annum 
in expense for oil produces a net loss of over $11,000. Such 
cases have probably frequently occurred. On the other hand, 
it is sometimes found that the cheaper oil is also that best 
suited to the work, and a gain is effected both in cost of oil 
and in expense of power. 

In illustration of the application of the method just de- 
scribed to railroad practice, assume an oil to be used costing 
$0.35 per gallon, and giving a mean coefficient/", = 0.01, the 
cost of work and of wear, and of that part of the fuel used on 
the engine, in overcoming the resistance of lubricated surfaces, 
which may be taken as two thirds the whole quantity burned, 
for example, to be $0.20 per mile, and the quantity of oil used 
per mile to be 0.02 gallon. 

Then the total expense per train-mile to be charged to the 
lost work of friction is (Eq. 13) 

Ki — K<li + dfi — °- 2 5 X 0.02 + 20 x 0.01 = $0.20^, 



jr j 0.20 g. 

as since af t = 0.20, a = — — = $20. 






358 FRICTION AND LOST WORK. 

Oils causing serious wear should always be avoided, how- 
ever and cases of such wear may be left out of the account.* 

Were it proposed to use an oil costing k^ = $0.10 per gallon, 
at the rate of q 2 = 0.04 gallon per mile, with a value of 
ft = 0.02, the cost would be 

K* — K<1* + ^/ 2 = o.iox 0.04 + 20 X 0.02 = $0.404 ; 
K x -K,= -$0,199, 
while the saving in cost of oil would be 

KQx — K<1* — 0.005 — 0.004 = $0,001. 

Saving one mill in buying oil, the amount lost on the 
coal account would be 20 mills, or twenty times that "saving." 
The apparent gain of 20 per cent, in cost of oil is enormously 
overbalanced by the increase of 100 per cent, in other expenses 
of overcoming of the friction of lubricated parts. All these 
figures will vary greatly for different cases ; but the general 
conclusion remains as already stated — the relative cost of good 
lubricants is a comparatively unimportant matter. 

Pure lard-oil would probably be best here taken as a stand- 
ard for comparison. 

The experiment was recently tried, on one of the great 
" trunk-lines" in the United States, of using pure lard-oil in 
summer and the best of sperm-oil in winter on freight-trains, 
employing one person to attend simply to their lubrication. 
The number of cars which could be hauled by each engine was 
thus increased about 10 per cent., and much greater regularity 
of service was secured. The saving effected in cost of trans- 
portation was sufficient to pay double the total cost of oil used 
and labor employed. In another case in which 50 per cent, 
more was paid for one oil than for another, the higher-priced 
oil was found very much the cheaper, on the score of saving 
the expense of hot journals alone. 

154. The Conclusions to be drawn from the preceding in- 

* In some cases, using crude and black petroleums, the cost of wear is but 
little less important than that of power. 



THE FINANCE OF LOST WORK. 359 

vestigation are obvious : — The art of economical employment 
of lubricants consists mainly in the determination of their 
adaptation to specific purposes, and in the application to each 
machine — or to each part of a machine in which pressures on 
lubricated surfaces of widely differing amounts are found — of 
precisely that quality of unguent which is best adapted to that 
particular place, and, above all, applying it in the best possible 
way. 

It is uneconomical to use a spindle-oil for the crank-pin of a 
steam-engine, or for the pivot of a heavy swing-bridge ; to apply 
an engine-oil to a sewing-machine, or light machinery-oil to the 
journal of a railway-train. In a cotton-mill or other large man- 
ufacturing establishment, the parts of the engine, its steam- 
cylinder, guides, and connecting-rod journals, the heavy and 
the light line-shafting and the counter-shafting, as well as the 
several kinds and the several parts of the working machinery, 
may often be found to be best lubricated with different oils. 

The price of lubricants is usually a matter of little interest 
to the user except when oils of substantially the same quality 
are to be compared ; and whatever may be the price, an oil or 
a method of lubrication producing serious wear should not be 
used at all. 

The determination of the qualities of the several grades of 
lubricants obtainable in the market must usually be made by 
the use of a good form of lubricant-testing machine, and 
should include a determination of wear of rubbing parts. No 
difficulty need be experienced in this investigation in deter- 
mining the friction and endurance of any oil under specified 
and obtainable conditions ; but it may often happen that seri- 
ous difficulty may be found in the attempt to identify the 
precise conditions of application, or to measure the wear of 
journal and bearing. 

It is important that this method should be applied to each 
department, and in each application of the lubricant in every 
establishment, and the relative cost of power saved, and of 
lubricant expended, be thus ascertained. When the market 
shall have finally become so well settled that prices of good 
oils have a direct and stable relation to their intrinsic qualities 



360 FRICTION AND LOST WORK. 

and to the demand, this method of investigation will lead to a 
definite policy in every case in the purchase of lubricants. 

One of the important deductions from what has preceded 
is the conclusion that for any given case of application the 
principles here developed, coupled with a correct system of 
test, will enable the consumer often to secure, by experimental 
mixing of oils, precisely that combination of qualities which 
best suits the conditions given. The Author has sometimes 
found this process to yield economical results of great financial 
importance. 

The use of the testing-machine to determine the relative 
friction-reducing power and wear, and the endurance of oils as 
data for use in the solution of the commercial problem, will 
often be found to involve some difficulties. These difficulties 
arise, however, not from faults of the method, but from the 
exceedingly great uncertainty often existing as to whether the 
conditions of test are precisely those of use. A good testing- 
machine may be relied upon, if properly handled, to give accu- 
rate data ; but it can rarely be made equally certain that the 
same conditions can be permanently retained when the lubri- 
cant is put in service. Satisfactory approximations may, how- 
ever, readily be secured with careful supervision and ordinary 
skill, for all cases in which the machinery is well proportioned, 
in good order, and well cared for. 



INDEX. 



ART, . PAGE 

Acceleration and retardation 9 g 

Acid-tests of oils 108 201 

Adulteration, detection of go 154 

Ashcroft oil-testing machine , 129 247 

Bailey's viscosity-apparatus 104 ig4 

Baume's scales of density 100 185 

Bearings, cooling 87 150 

" surfaces for 88 150 

" water 86 150 

Belts and cords, friction of 31, 118 64, 220 

Bochet's experiments I3g 305 

Brakes, friction of 117 216 

Carriages, resistance to traction 114 208 

Cartwright's curves I3g 313 

Castor-oil 70 126 

Chateau's tests of oils g4 158 

Chemical tests of oils gi 155 

Clark's experiments on train-resistance. 115 211 

Cocoa-nut oil , 67 125 

Coefficients of friction 134 272 

Cohesion-figures no 204 

Cold tests of oils 107 200 

Collars and pivots, friction of 30 54 

Colza-oil 65 124 

Congelation temperatures of oils 107 200 

Cordage, rigidity of 34 75 

Cords, resistance of 31 64 

Cotton-seed oil 63 123 

Coulomb's experiments 75, 114 130, 208 

Cups, oil and grease 81, 82 141, 143 

Density of lubricants, and friction 45 g8 

" of oils gg 184 

" scales of Baume 100 185 



362 INDEX. 

ART. PAGE 

Density scales of commerce 101 187 

Drying of oils. , 103 192 

Earth, friction of . . 41, 123 85, 231 

Effort, denned 6 6 

Elaine-oil 68 125 

Electricity, tests of oil by in 205 

Energy, defined , 7 6 

' ' persistence of 8 8 

' ' potential and actual , 7 6 

' ' storage and restoration 10 9 

' ' wastes of 49 102 

Equilibrium and motion, principles, 24 23 

Fire-tests of oils 106 198 

Fish-oils 60 119 

Fluid-friction 43, 44, 120 96, 97, 225 

Forces, defined 6 6 

' ' driving 6 6 

" frictional 15 15 

" moving and resisting 15 15 

Friction, angle and cone of 20 20 

1 ' causes and kinds of 14 14 

coefficients of 18 17 

" kinetic, or friction of motion 22 20 

laws of sliding 17 16 

lost work of 13 12 

machinery and mill- work 13 12 

method of measuring coefficient 19 18 

motion 22 21 

" reduction of 12 10 

" rest 2i 21 

rolling ..16,36,37 16,79 

solids, sliding 16 16 

" static 21 21 

Foundations 41 85 

Gases, friction of 121 226 

Gearing, friction of 33, 118 73, 220 

" "worm 126 235 

Graphite 55 115 

Grease 54 113 

" cups 81 141 

Gumming of oils 103 192 

Heat, effects of 105 196 



INDEX. 3 6 3 

ART. PAGE 

Internal friction 46 99 

Jenkin's experiments 139 308 

Journals, friction of 29, 126 40, 235 

length of 29,127 40,239 

Kimball's experiments 139 306 

Lard-oil 58 118 

Linseed-oil 71 127 

Liquids, friction of , 122 227 

Lubricants, characteristics and uses of 50, 51, 52 104, no 

' ' relative endurance of 136 284 

" " standing of 135 280 

" solid, use of 78 138 

Lubricated surfaces, friction of ... 125 233 

Lubrication 47 99 

methods of , . . 77, 78, 79 137, 138, 138 

of moving parts 83 146 

Lux's improvement on Thurston's machine 131 266 

Machinery and mill- work, lost work in 13 12 

' ' classified 2 1 

" power demanded by ,, 3 2 

work of 2 1 

Machines for testing lubricants 112, 128 205, 243 

Materials of bearings 88 150 

Mechanism, efficiency of 12 10 

uses of 1 1 

Metals, action of oils on 97 179 

Metcalfe's testing-machine 128 243 

Mineral oils, impurities in 98 182 

Molecular friction 46 99 

Morin's experiments 114, 125, 126 208, 233, 235 

Nasmyth's viscosity apparatus 104 194 

Neat's-foot oil 59 119 

Oiling, methods of 80 139 

Oil-pumps 85 149 

Oils, animal 56 117 

" classed 52 no 

" method of examining 89 153 

" mineral 72 127 

" mixing 76 133 

1 ' vegetable 61 120 

Oleography 109 202 

Oleometers 99 184 

Olive-oil 62 121 



364 INDEX. 

ART. PAGE 

Palm-oil 66 124 

Pea-nut oil 62 121 

Petroleums 72, 75 127, 130 

Pivots and collars, friction of = 30 54 

Power denned 5 5 

" demanded by machinery 3 2 

Pressure, distribution of, on journals 28 37 

" limits of 48,127 101,239 

" variation with friction 137,138 296,298 

Pulleys, friction on 36 79 

" " of systems of 37 79 

Pump-pistons, friction of 119 224 

Pumps, oil 85 149 

Railway-train resistances 115 211 

Rankine on length of journal 127 239 

Rape-seed oil. 64 123 

Reactions of the oils 94 158 

Reagents for testing oils 93 157 

Remont's tests of oils 95 164 

Rennie's experiments 116 215 

Resistance defined 6 6 

Rest and motion, and friction 140 315 

Retaining walls, pressures on . - , 42 89 

Retardation and acceleration 9 9 

Riehle oil-testing machine 129 247 

Riveting, friction of 117 216 

Rolling friction 114 208 

Screws, friction of 32 71 

Screw-gearing, friction of 33 73 

Shafting, friction of 29 40 

Shale-oils 74 129 

Slide-valves, friction of ... 119 224 

Solids resting on rough surfaces 25 22 

" moving " " 27 30 

Specific gravities of oils 100 185 

Speed, condition of uniform 10 9 

Sperm-oil 57 117 

Stillwell's densities of oils 101 187 

Tallow 53 112 

" oil 59 119 

Temperature and friction 141, 142 319, 322 

Testing-machines for oils 112, 128 205, 243 

" Thurston's 130 254 

" use of 132 266 



INDEX. 365 



ART. PAGE 

Thurston's conclusions as to use of unguents 145 340 

formula for length of journal 29, 48, 127 40, 101, 239 

oil-testing machines 130, 131, 132 254, 266, 266 

on values of lubricants 146-154 360 

records and report . 132 266 

" tests of oils 134, 136 277, 284 

" effect of pressure 137 296 

" temperature 141,142 319,322 

" " " velocity 139 305 

" theory of the finance of lubrication 146-154 343-368 

Tower's experiments 143 332 

Train-resistances on railways 115 211 

Units of measure of values of oils 151 352 

Value of lubricants, conditions affecting , . 146, 152 343, 353 

Variations of friction 133 274 

Vehicles, draught of 40 84 

Velocity and friction 129 247 

Viscosity and density of oils 45, 102 98, 189 

Waite's experiments 14.1 319 

Walls, pressure on retaining 42 89 

Watson on action of oil on metal 97 179 

Water-bearings 86 149 

Wear, method of 28 37 

Wedges, friction of 32 71 

Well-oils 73 129 

Whale-oil 57 117 

Woodbury's experiments 137, 139 296, 305 

141, 143 3I9» 338 

oil-testing machine 129 

Work defined 4 3 

" diagrams of 4 3 

" of friction „ 13 12 

" of machines , 2 1 

" lost n 10 

" useful 11 10 



INDEX TO ADVERTISEES. 



PAGE 

American Lubricating Oil Company, - v 

Borne, Scrymser & Company, - i 

Cleveland Refining Company, ------ ix 

Columbia Refining Company, ii 

Crew, Levick & Company, ---,„.. iii 

Davis Oil Company, -------- yi 

Downer Kerosene Oil Company, ----- iy 

New York Refining Company, vii 

Pratt & Whitney Company, ------ viii 

Stuart, D. A., & Company, - vii 

Vacuum Oil Company, ------ vi 

Wiley, John, & Sons, ----- ix 



Extra Breton Oil for Wool 

Superior to the Animal and Vegetable Oils for greasing ivool, 
as it has no affinity for oxygen, does not gum, and scours 
with soap at about two degrees strength. Tarn will spin fine 
and regular. Piece dyes will take better color than with 
any oil used for oiling wool. 



Price, 45 cents per Gallon. 



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OILS FOR WOOL 




A SPECIALTY. 



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PARAGON WINTER CYLINDER OIL 

Price, 85c. per gallon. 6oo° fire test. 
Good cold test. The best Cylinder 
oil in the market. 

650° F. CYLINDER OIL. 

Price, 65c. per gallon. Very heavy body. 
Possesses great endurance. Feeds 
perfectly through patent cups. 

PARAGON ENGINE OIL 

Price, 60c. per gallon. A very viscous 
oil, adapted for the heaviest work. 

BRILLIANT MACHINERY OIL. 

Price, 40c. per gallon. For general lu- 
bricating purposes. 



CRYSTAL LOOM OIL 

Price, 70c. per gallon. Equal to Sperm 
as a standard oil for Looms and Knit- 
ting Machines. 

STAINLESS SPINDLE OIL 

Price, 30c. per gallon. Specially adapted 
for use in Woollen Mills. Will wash 
out perfectly. 

PARAGON SPINDLE OIL 

Price. 25c. per gallon. Combining ex- 
cellent body with small viscosity. 
Adapted for use on the lightest Cot- 
ton Spindles. 



BORNE, SCRYMSER & CO., 

Works : Elizabethport, N. J. 224 Front St., New York. 



Send for our Circular giving full information on the subject of OILS for WOOL. 
A trial invited. If not satisfactory, return goods at our expense. 



1 

383 & 385 West 12th Street, 

NEW YORK, U. S. A.. 



MANUFACTURERS OP 



MINERAL 



Lubricating Oils, 



LUBRICATING COMPOUNDS, 



-AND- 



Car, Coach, Axle, Wire $ Mill 



CREASE. 



SE1STD FOR CIRCULAR AND PRICES 



Ill 



CREW, LEVICK & CO., 

ESTABLISHED 1865, 

PHILADELPHIA, PA., 

PROPRIETORS OF THE 

SEABOARD OIL WORKS, 

REFINERS OF SPECIALTIES IN 

Hi£k Fire Test Petroleim Products 

OF THE FOLLOWING 

RED LETTER BRANDS: 

RUBY MACHINERY and SPINDLE OILS, 

Red R. — Odorless, nearly Double the Viscosity of Pale Oils, 
and Higher in Fire Test. Require no Compounding. 

CYLINDER OILS, 

Steam Refined.— Red P and Red M. Heavy in Body. 550 to 600 Fire Test. 

FILTERED CYLINDER OILS, 

Red F. — Extra Light in Color. 500 to 600° Fire Test. 



Specially Prepared Cold Test Cylinder Oils. 

MONARCH VALVE OIL, 

Red V.— 600 ° Fire Test. 

LOCOMOTIVE CYLINDER OIL, 

Red L. — 600 Fire Test. 

STAINLESS WOOL and BATCHING OILS, 

Red W.— Will Saponify Perfectly. 

COLD TEST FILTERED NEUTRAL OILS, 

Red N. — Bloomless, sweet in odor, Sun Bleached and Low Cold Test. 

SPERMOLINE BURNING OIL, 

300 Fire Test. 



High Fire Test Mineral Lubricating Oils, 

» ♦ • 

From 120 to 130 Melting Point. 



IV 



Downer Kerosene Oil Co., 

104 Water St., Boston, Mass. 

NEW YORK OFFICE, 113 MAIDEN LANE. 

MANUFACTURERS OF THE 

PRODUCTS of PETROLEUM. 

Proprietors of the Standard and Well Known Brands 

AND 

IMLAJDE ESPECIALLY IFOE, 

Cotton and Woolen Machinery 

By our own Patented Processes, which alone ensure 
ABSOLUTE UNIFORMITY. 



CHAMPION OIL, 

Of Great Body and Unequalled as a 
LUBRICANT FOR HEAVY MACHINERY. 



For Sewing Machines and other Light Machinery, 
and for Oiling Wool. 



DENSOLEUM, 

1 6° GRAVITY. 

These Oils are everywhere acknowledged as the Most Reliable and 
of the Finest Quality made. 



V 

Capitol Cylinder Oil. 

CAPITOL CYLINDER OIL is manufactured by the American Lubricating Oil Company, 
Cleveland, Ohio. 

CAPITOL CYLINDER OIL has been in use Ten Years ; it is therefore no new thing— no 
experiment. It gives satisfaction. 

CAPITOL CYLINDER OIL is made on scientific principles. There is no guess-work 
about it, but careful study, experiment, and test. 

CAPITOL CYLINDER OIL is made from the very best selected crude petroleum, manu- 
factured by the most approved processes. 

CAPITOL CYLINDER OIL stands a very high fire-test, about 6oo° Fahr., and therefore 
will not evaporate or waste in the cylinder, however hot the steam may be. 

CAPITOL CYLINDER OIL prevents corroding of the metal, gumming of the valves, etc. 

CAPITOL CYLINDER OIL is a trade-marked brand, and every barrel has a paper label 
on the head bearing the full copyrighted brand, containing a correct view of the National 
Capitol at Washington. If you buy this oil be sure that this paper label is on the package, as 
otherwise the oil is not the genuine CAPITOL CYLINDER OIL. 



What Marine Engineers say of Capitol Cylinder Oil. 

Cleveland, O., December 23, 1884. 
Gentlemen : In reply to your request I will state that I have used your Capitol Cylinder 
Oil for the last year on a compound engine, cylinders thirty and fifty-six inches in diameter, 
and it gave entire satisfaction, and I can cheerfully recommend it as the best oil I have ever 
used. Respectfully, J. Rigg, Chief Engineer Steamship Wo Co Ken. 

December, 1884. 
Dear Sir: The Capitol Cylinder Oil I have used for the last three years, and have secured 
better results from it than from any cylinder oil I have ever used. 

W. H. Seeman, Chief Engineer Steamship A. Everett. 
Cleveland, O., Decembers, 1884. 
I have used your Capitol Cylinder Oil for three years, and in that time I have used, or 
rather tried to use, several other brands of oil, and never found any to come anywhere near 
to the Capitol Cylinder Oil. It keeps the cylinder and rings always clean and free from gum. 
I have used it with a pressure of 60 to 140 lbs. of steam and it never failed to do its work with 
me. It is the best cylinder oil manufactured. Respectfully, 

J. B. Miller, Chief Engineer Barge Business. 
December, 1884. 
I have used the Capitol Cylinder Oil for five years, and find it to be a splendid lubricant 
on both compound and high-pressure engines. Respectfully, 

W. S. Semple, Engineer Steamer H. L. Worthington. 



Eldorado Engine Oil. 

Prof. Thurston's Report of Eldorado Engine Oil. 

Stevens' Institute of Technology, Hoboken, N. J., Feb. 9, 1883. 

A comparison of the results obtained from tests of ELDORADO with those obtained at 
the same time from "Standard Laboratory Lard Oil " leads to the following conclusions: 

With a free feed and a pressure of 100 lbs. per square inch and a speed of 250 revolutions 
of the test-journals, the minimum coefficient of friction was about six-tenths of one per cent, for 
ELDORADO ; the minimum coefficient of friction for lard-oil was seventy-three one-hundredths 
of one per cent, (the average being eighty-two one-hundredths of one per cent.) 

The oil is therefore superior to lard-oil for reducing friction ; reducing the friction ob- 
served for lard-oil about twenty per cent. 

When a weighed amount (eight milligrams, about one drop) of each oil was placed on the 
test-journal and the machine started and run. as in the case of a free feed, the number of revo- 
lutions made by the test-journal before the oil ceases to lubricate or wears out, will give what 
is known as our "endurance-test." The coefficient of friction is, of course, larger in this 
case than with a free feed or the " friction-test." 

The record shows that the lard-oil endured through 10,000 revolutions, while ELDORADO 
continued to lubricate up to about 13,000 revolutions, giving at the same time a lower co- 
efficient of friction. 

In brief, the oil may be rated as 20 per cent superior in reducing friction, and 30 per cent 
more enduring thafi pure lard-oil for ordinary speeds and pressures. 

The oil is more viscous than lard-oil, and during the " free-feed " test we used less oil. 

We find, on referring to the similar test made last summer, that the results obtained then 
are practically the same as now. R. H. Thurston, Director. 

ELDORADO ENGINE OIL, MANUFACTURED BY 

The American Lubricating* Oil Company, Cleveland, Ohio. 



VI 
THE BEST IS ALWAYS THE CHEAPEST, 



For Nineteen Years 

VACUUM OILS 

Through superiority of process and care in manufacture, have led 
all others, affording 

Perfect Lubrication at Lowest Cost. 

THEY SAVE MONEY, 

SAVE POWER, 

SAVE FUEL, 

SAVE MACHINERY. 

Send for new Pamphlet Circular with Autograph Testimonials. 

VACUUM OIL CO., Rochester, N. Y. 

51 Purchase St., Boston ; 96 Water St., New York ; 70 St. Peter St., Montreal. 

THE DAVIS OIL COMPANY, 

MANUFACTURERS OF 

LARDIEENEATSFOOT OILS, 

SOLE MANUFACTURERS AND PROPRIETORS OF 
WELL-KNOWN BRAND, 

"DAVIS' REFINED OILS." 



Our Oils are especially adapted for Compound- 
ing purposes and Export. 



PURITY and QUALITY GUARANTEED. 



Works : Brooklyn, N. Y. Office : 37* Water Street, New York, 

CHAS. W. HAND, Manager. 



D. A. STUART & COMPANY, 



MANUFACTURERS OF 



Oils $ Lubricating Compounds, 

CHICAGO, ILL. 



Send for Descriptive Price List. 



Dealers who furnish Consumers with Lubricants are 
invited to send for sample, etc., of 

STUART'S CASTOR GREASE. 

JAS. H. PLATT, Prest. G. C. THORP, SecV. 

ANDREW WASHBURN, Vice-Pres't. G. S. RICHARDS, Treas. 

NEW YORK REFINING CO., 

141 Maiden Lane, - New York. 

FACTORY : Newtown Creek, Blissville, L. I. 
MANUFACTURERS OF 

Pure Mineral Lubricating Oils 9 

CARBOLINE CYLINDER OILS, 

CARBOLINE MACHINERY OILS, 

CARBOLINE ENGINE OILS, 
PURE FARAFFINE OILS, 

BLACK OILS, SIGNAL OILS, 

STANDARD LUBRICANTS, 

PURE MINERAL GREASES, 

For all kinds of Machinery. 
AXLE GREASE and CARRIAGE LUBRICANT. 



Owners of Machinery will find it to their advantage to communicate directly 
with us in the selection and purchase of their Lubricants. 

♦ 

SPECIAL CONTRACTS WITH LARGE CONSUMERS. 



vm 

-Hie T ISC IE ?N- 



PRATT & WHITNEY CO., 

HARTFORD, Conn., U. S. A., 

MANUFACTURERS OF 

MACHINE TOOLS 

For RAILWAY and GENERAL MACHINE SHOP SERVICE, 



-AND- 



Special Machinery. 

MACHINERY & SPECIAL TOOLS 

FOR 

Armories, Sewing Machine and Agricultural 
Implement Manufacturers, 

ROLL GROOVING MACHINES 

For Fluting Chilled Rolls for Flouring Mills. 



U. S. STANDARD TAPS and DIES, REAMERS, GAUGES, 

FIXTURES, and ALL TOOLS necessary for 

INTERCHANGEABLE WORK. 



Also, Manufacturers of Prof. R. H. Thurston's 
PATENT 

R. R. Standard Lubricant Testing Machine. 



SEE FRONTISPIECE. 



Illustrated Catalogue and Price Lists furnished on application. 



IX 



The Cleveland Refining Co. 

Works and Office, Bessemer Ave. and C. & P. E. R., Cleveland, 0. 

PETROLEUM AND ITS PRODUCTS 

Lubricating Oils, Naphtha and Gasoline. 

Water White Diamond Light Carbon Oil a Specialty. 

RAILROADS WILL PLEASE NOTICE 

That we make a Specialty of soliciting their Trade for either 
Lubricating or Burning Oils. 



THE NEW AND COMPLETE CATALOGUE 

OF THE 

PUBLICATIONS 

OF 

JOHN WILEY & SONS 

15 ASTOR JPJLACE, J\JEW YORK, 

CONTAINING 

Scientific and other Text-Books for Colleges, Industrial Schools and Theological 
Seminaries, with many Valuable Practical Works for Architects, 
Engineers, Mechanics, etc., 
Including Works on Agriculture, Assaying, Astronomv, Book-keeping. Chemistry 
Drawing and Painting. Electricity, Engineering. 'Metallurgy, Machinery, 
Mechanics, Mineralogy, Seamanship, Steam-Engine, 
Ventilation, etc., etc., 
And for Theological Seminaries. Hebrew and Greek Bibles. Testaments, Lexi- 
cons, Grammars, Reading-Books and Concordances. 

Also a full List of their Editions of 

JOHN RUSKIN'S WORKS. 



Will be sent free by mail to any one ordering 1 it. 



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